When you mention bandages, are you talking about using KT tape? It seems like that works pretty well, although I haven't tried it personally.
There are also compression undershirts for cis men with gynecomastia, which I imagine are accommodating of a larger ribcage.
Another consideration is, do you actually have to go visit your parents, or do you just feel obligated to? Do you have to stay with them, or could you stay in a hotel instead?
For how long will you be visiting them? If you're going to be there for multiple weeks, pre-preparing syringes probably isn't a viable plan.
That sucks. Did you consider using estradiol undecylate? It has a pretty long half life and some people do monthly doses of it. Maybe you could do a large dose right before you leave on each trip? Even if it doesn't last for the entire time you're gone, you would be without estrogen for a shorter period of time.