Dear Samuel,
Here are my suggestions:
1. The phrase "Rejoice, O honourable Prophets" in the beginning should not be broken down into two pieces by using two sticheraric formulas. Hypothetically, since there is a comma in the phrase, it could be broken into two separate phrases, but only if the break is placed where the comma is. I don't think it is right to put the break after the word "O", so I suggest simplifying the melody for the first few syllables and making them into a "heirmologic bridge". One possible solution would be:
Re- Di
joice Ke
O Di
2. It isn't easy to decide whether the word "honourable" should be treated as a four-syllable word (hon-our-a-ble) or as a three-syllable word (hon-'ra-ble). I find that treating it as a three-syllable word usually makes the melody sound better to my ears. I would suggest deleting the "our-" syllable, and changing the "a-" syllable to " 'ra-" with an apostrophos and a klasma.
3. The next phrase "who have rightly ordained the law of the Lord" is broken into two pieces after the word "the". If this phrase is going to be broken into two pieces, the break needs to be placed such that the groups of words before and after the break express a complete phrase. So instead of the two sub-phrases being: "who have rightly ordained the" and "law of the Lord", they should be: "who have rightly ordained" and "the law of the Lord".
To implement this grouping of words, we will need to find a 001001 formula for "who have rightly ordained". There are three of them on p. 107 in my collection of my formulas. If we use one of the first two of those, we would need to remove the klasma from the last note so that it would blend in with the following words. Then, we can put the word "the" on Ga followed by "Law" on Di (an oligon with a klasma), and then the rest of your melody for that phrase works fine.
4. The melody for the next phrase "and were revealed to be inviolate" works fine as a bunch of filler notes. But one thing have I noticed about sticheraric second mode (unlike other sticheraric modes) is that it rarely has that many consecutive syllables, each with one note. There is a much greater tendency to break phrases down into smaller pieces, each with its own sticheraric formula.
Bearing this in mind, we should find a sticheraric formula for this phrase, which has a 0001000100 accentuation pattern. On pages 105-106 there are several options to choose from, but I think the X000100 formula would work best. To unite this formula with our text, we can keep your melody for "and were re-" as it is, and then for "vealed" we will use an oligon with a psefiston.
One minor improvement to your melody for "and were" is to replace the two isons you have for these words with an apostrophos and an oligon, so that the melody goes:
and Pa
were Vou
This is an improvement because in this mode, when a phrase that begins with an unaccented syllable is preceded by a martyria on Vou, that unaccented syllable is usually written as an apostrophos (descending to Pa for one beat).
5. The melody for "unshakeable" is okay, but it's rather bland. Considering that the melodies preceding this phrase have not ascended to Zo for a while, it would sound better to get a Zo in there for some variety. This can be done easily by using one of the 01001001 formulas on p. 112 for the words: "unshakeable pillars in faith". The preceding two syllables "and" and "un-" can be single-beat notes on Di and Ke respectively.
6. The last three lines on the first page have too many consecutive single-beat notes. Another problem is that the phrase "New Covenant of Christ" has a melodic break after the word "New". To fix these problems, I suggest breaking up the text into the following phrases:
(A) "for ye proved also to be mediators"
(B) "of the New Covenant of Christ"
Phrase (A) has a 00100001000 accentuation pattern. Since there is no such formula in my collection, we will need to break it down into smaller pieces. We can get away with breaking into "for ye proved also to be" and "mediators" if we make sure that the break between the two is not the kind of break that would necessitate putting a martyria there. To pull this off, we can use one of the 10001 formulas on p. 99 for "proved also to be" and the last 1010 formula on p. 106 for "mediators". The trick to make a smooth connection between these two phrase is to replace the oligon and klasma used for the word "be" with an oligon followed by kentemata. And then instead of jumping up two notes for the syllable "me-" (which is the first note in the last 1010 formula on p. 106) we only ascend one note.
If I have confused anybody, let me know, and I'll write out what I mean instead of trying to describe it.
As for phrase (B) ("of the New Covenant of Christ"), since it is followed by a period, we shouldn't end the phrase on Zo, but on Di or Vou. We haven't had an ending on Vou for several lines, so I think now would be a good time to use one. On p. 109, there are plenty of 10001 and 010001 formulas to choose from, all of which would work fine. Then we just use some filler notes for the first three words: "of the New".
7. In line 2 of page 2, the melody for the word "translated" emphasizes the syllable "lat-" instead of "trans-". So we will need to find a 100100 formula for this phrase "having been translated". There are three such formulas on p. 105. The melody for first of these has already been used earlier in our composition, so we don't want to use it and sound repetitious. The second one is also undesirable, because it ends with a melody that it usually used only just before a martyria, i.e., where there would be punctuation in the text. But since the phrase "having been translated" is followed by "unto Heaven" without any punctuation, this melody would be inappropriate. Therefore, our best choice would be the last of the three 100100 formulas on p. 105.
8. The original melody for this troparion has elaborate melody that holds the final syllable of "ouranon" (heaven) for 18 beats. It turns out that there is a similar melody that can be used for the word "heaven" on p. 124 in my collection of formulas: the first "10" formula on that page. (By the way, I just noticed a typo in that formula: instead of three consecutive oligons with a klasma, there should be only two.) To connect this melody with what precedes it, we can simply use filler notes for the word "unto", such as:
un- Di
to- Ke
9. The heirmologic bridge for the words "entreat Him to grant peace unto the world" would be fine in other modes, but because (as I mentioned above) second mode avoids having so many consecutive single-beat notes, I think it would be better to use a sticheraric formula for the first few words: "entreat Him to grant peace". We can use the first 10001 formula on p. 99 for the syllables "-treat Him to grant peace". But to join this melody smoothly with the following words, the klasma above last oligon of that 10001 formula should be deleted. Don't forget that deleting the final klasma in a formula is a common trick used in order to make smooth transitions.