If the font doesn’t include capitals and punctuation, the users will find themselves constantly switching fonts to type other text. Since a Unicode font can support many thousands of characters there is no problem including all of the regular characters as well as the phonetic ones.
This is why you need to develop and test the font yourself, to see if it is practical to type with. Autocorrect could play havoc with your method — ǎ might be converted to ā if it starts a sentence. Of course, users can turn off autocorrect, but ideally the font would not need too many special instructions, and would not be limited to use in Word, but would work equally well in any application.
Most are standard Unicode characters that you will find in Verajja, but dotless ı with a dot above is going to be confused with regular lowercase i. Only ȧ, ė, ȯ exist in Verajja IIRC.
You will also find the combining double macron and combining double breve. So too are upper and lowercase eng — Ŋ ŋ
Here is where it starts to get difficult. A combining slash could be used, but each letter is a different width, so the silent consonants really need to be designed as specific glyphs.
Is the use of slashed consonants standard practice in phonetics or your own invention?
I find that shift hyphen key is a logical choice for the macron dead key for typing ā ē ī ō ū.
Making it yourself is likely to be the only viable route. The design process could be very lengthy and costly. The Vera (and Verajja) fonts are released under GNU (copyleft) license. If you want to retain copyrights to your font, then you also need to design the basic alphabet shapes — a great deal of extra work — or find a suitable typeface that is in the public domain.
Using the standard UK or US keyboard strictly limits the number of letters that you can type. It also means assigning accented lowercase to uppercase, punctuation, and numerals, as you suggested. If the font needs specialised training and/or keyboard charts to use it, the likelihood of widespread adoption will quickly evaporate.
Take a good look at existing Windows keyboards, e.g. US International, French, or German keyboards to see how they work with dead keys. I suspect that using dead keys will be a more viable method of typing with your phonetic font, though it will require a customised Windows keyboard.
Finally, consider the extensibility of the font. If teachers want to type French, Spanish, or German words with phonetics, for example, how would that work?