Is there anything I can do here? Any help would be greatly appreciated.
Sorry, no. iTunes Match is not designed to be used the way you are using it. It is designed to be a single-user service that is always signed into the same iTunes Store account.
The easiest way to accomplish what you want to do is to update the app in iTunes (on your computer) then sync the app to your iPhone.
Oka, another question I have then, which is frustrating me beyond belief, is why, if is Tay logged into my match account, songs are oftentimes deleted from my phone?
I have a playlist of "new" music that has about 600 songs in it. That playlist will randomly dump hundreds of songs, leaving them to show available for download from match, but they are removed without me having deleted them.
Now, 2 things happen on my main PC where I set up match. The first is that randomly, with little fanfare, match will just shut itself off. No explanation, just stops.
The next is that I have multiple iTunes accounts and in order to update the apps in those accounts, I have to sign into another account, update, and then sign back in. Each time I have to turn match back on, which I do. It takes all of 2 minutes and according to a less than scientific test I just did, it doesn't seem to cause song deletion from my phone by doing this.
I'm getting very frustrated that a service I pay for, while being somewhat convenient from time to time, is causing nothing but problem upon problem. I can't be the only person juggling multiple iTunes accounts on each device, can I? =\