Implants are typically not done until you've been on T for a year, as I understand it. I'm not sure if that's everywhere, but that's what I've been told.
I'm sorry you're having issues with Chase-Brexton. How far from DC are you? I go to Whitman Walker and have never had any issues. It may be a bit of a hike though depending on where you're coming from, especially if you want to get injected weekly. But I really can't recommend them highly enough. They've taken care of my T, all my surgical referrals and aftercare, etc. The pharmacy there is also considerably less expensive than CVS, Walgreens, etc.
You could also look into the price of Testim. It's also a topical form of T and is generally cheaper than Androgel. Looking it up on GoodRx right now, it's about $160 per month, as opposed to the $450 of Androgel. For me, that is still prohibitively expensive. But it may be an option for you, especially if you take the time you would spend driving to the doctor's every week into consideration.