Not enough AP classes? (Unique circumstance)

Okay, so my situation is kind of unusual. I came to the US when I was 17 and joined my junior year (2016-2017) here. I went from a completely different UK Curriculum (AS level) to the US education system, so there were a lot of things I had to learn to adjust to. Unfortunately, when selecting my classes for junior year, I didnt take nearly as many APs as I should have. I had never heard of APs before, and my counselor didn’t inform me about them either (so basically it was like a first-time introduction to APs in junior year!). So i ended up taking only AP Bio and PreCalc Honors. Halfway through the year, I find out APs are actually essential for getting into a good college with scholarships and all, and I’m really upset…but it’s too late to take AP classes now. I’m taking 4 APs senior year (AP Psych, AP Calculus BC, AP Chem/ APES and AP Gov) but I know colleges don’t look at senior year.
I am a pretty good student, i’d say.
My unweighted GPA (as of right now): 4.00
Weighted GPA: 4.50
My PSAT score was 1400 and I’ve registered to take my SATs on June 3rd; I’m expecting a very good score.
I’ve joined clubs and am dedicating my time to volunteering as much as I can.
My school is very competitive, offering about 20 APs. I know I compare poorly to my peers who are at the top, but my circumstances are completely different. I didn’t have time to transition from one to two to multiples APs like most of the people at my school. I’m aware colleges look at each situation differently…so do you think in my case, they’d excuse the lack of APs if I explain my circumstance to them? Exactly how important are AP classes? Don’t other things such as test scores, college essays and ECs matter too?
P.S. I plan to apply to Rice (along with other safer options of course) but I can’t afford it without scholarships.

All I can say is my son got admitted to the very selective UCLA CS major for fall 2017 with 0 AP’S. Now he was in a non traditional school that didn’t offer them but took most challenging courses his school did offer.