Well, you seem to be in the "sports bra" zone to me. To that end, you're also likely going to need trial-and-error if this is the way you want to go. Based on your post, I don't think you are anywhere near the "legit bra" zone; you're probably just in need of some compression to attain the comfort you seek.
In my experience, many/most (OK, all) female sports bras will also dig in under the arms when worn by a man, this might be something you need to get used to for a while if this is your path forward. The garments are designed for women, who tend to have a notably smaller underbust (32"-38" as opposed to our 38"-44"?) and a notably larger actual bust than we will. It's pretty easy to visualize the conundrum; the garment would "boomf" out much more for a woman and stretch away from her armpits, but it's also designed to conceal the side breasts of a woman, so the manufacturers can only make those armpit holes so big. Put that same sports bra on a man, understanding that we need to use the bigger sizes to accommodate our larger underbust, and it just doesn't work the same way. At this point of your journey, you simply do not have enough physical tissue to push that garment forward and pull it out of your armpit.
Unless you opt into surgery and are being monitored by a physician, I think you should avoid ACE bandages or a surgical-grade compression vest (binders). Both of these options can cause you more physical harm than good. To that end, have you consulted with your PCP?
Can't speak to dealing with clasps, but dealing with taking on/off a sports bra (racerback or not) seems pretty straightforward to me; pull it off the opposite of the way you put it on? I imagine that clasps are best handled by rookies like us by moving said clasps around our body to be on our chests and just ... unclasping them? Have never had any problems removing a racerback sports bra myself; just undo what you did.
If you are looking for a sports bra suggestion, I found my best "solution" with Oalka Sports Bras, which seem to be only available from Amazon.
To me, your best option is to go back to the retailer, vocalizing your complaints, and seeing what they can do for you.