I did track and field, JC level, two years of D1, a year on the Euro circui, and Master's level these days.
Diabetes is not a reason to give up on competitive athetics. There are too many of us competing successfully at all levels, from weekend warrior up to professional ballplayers, for you to think that you are alone in this and hopelessly in over your head when it comes to playing basketball and controlling your diabetes.
Yes, hypos are scary as hell, especially during work-outs and competition, but if you are spiking to 300 and 350 after workouts/competition, you have lot's a room for adjustment while still being able to maintain near normal BGs.
Honestly, it sounds like turning down your basal, popping glucose tabs, and drinking gatorade at the start of your 25 minute physical activity is way overkill. Msssing with your basal is tricky because it may take up to three hours to see an affect after you've made an adjustment. You may have turned down your basal right before your work-out, but IOB would take you straight through your 25 minute exercise, then leave you high and dry with a decreased basal just when you need a bigger dose the most to bring down a post-exercise glucose dump from your liver.
Look at this as being a trial by fire for the rest of your life. You need to do some serious BG testing during your workout to see exactly what your BG profile is under physical stress. Don't fly blind. You have to take the minute to test your BGs here and there when needed and I'm thinking that doing that will have minimal impact on your ability to play competitively. Make the adjustments, then assess again. Give yourself some latitude when it comes to BGs during execise and games if you have to as long as you can avoid those spikes above 200 and 300 post competition.
I'm not going to tell you to hang in there because that's not even an option for diabetics. Yeah, you can give up on competitive physical activities and work just to keep your BGs under control, but you don't have to. What you're gonna have to do is work a lot harder than non-diabetics to do the same things.
No, it's not easy to deal with diabetes and do anything that takes you out of a consistent routine but, honestly, your only choice if you plan on giving up on something you love to do now is to sit down and make a long list of the other things you plan to give up because of diabetes.
Let us know how things are going.