Plenty of exchanges out there. Tried any of those? Localbitcoins if you want to be completely anonymous, though fees are pretty high. I only used them to sell.
Honestly, maybe I'm not the best person to give you an answer, I haven't actually bought any btc in over a year.
Though I have to ask what exactly you mean by high limits. IIRC, Circle limited you to something like $300 a week