We are the main Testnet exchange at
https://altquick.com/exchange/ for both v3 and v4 Bitcoin Testnet. (I say main because we allow both buying and selling to let the market find the price.)
You can use the exchange without registering and convert the SOL to Testnet using
https://altquick.com/swap/, but please keep in mind it uses the books to trade on our site only (so review the books first and pray like hell they don't fill before you confirm!). $50 should be dust and move right through the system and you'll have a ton of Testnet coins in <10 minutes.
If you want testnet coins you'll need to buy them-- that's a consequence of a market existing for them.
A consequence of our market is that people can actually get them period. Bulk for pay or dust for free. With a sustainable business model.
When I first got involved with Cryptocurrency, I had to use Bitcoin because Bitcoin Testnet was, as the OP says, laughably difficult to get.
We also do support a free testnet faucet
https://altquick.com/faucet/. You can claim 0.01 Testnet of either version every ten minutes. The cost to withdraw is 0.01 Testnet, so in 20 minutes and two captcha solves you'll have free coins on chain.
Free Testnet is still available for both v3 and v4 with AltQuick, but we are having difficulty marketing due to our taboo market pairs. (Which I understand, but I still believe AltQuick deserves to be listed as a Testnet v3 & v4 faucet option on the
Wiki.)
Happy to send you some for free with our automated faucet, or if you want 100,000 coins in 15 minutes... we can accommodate that for either version. I'm sure
https://coinfaucet.eu/en/btc-testnet3/ and
https://coinfaucet.eu/en/btc-testnet4/ work fine too faucet wise.
You can still totally mine v4 50tbtc reward blocks... but it is likely far faster & cheaper for us to buy them, unless you know how to "fancy mine". Which will hopefully be patched early january according to the Bitcoin Mailing list thread about "unbreaking testnet".
I threw a rented miner and hit a block with an normal pool too.
block 100680 tb1q9qa5vcsz2nwd3etl46y56z7ckj75zjd5e8c5z3 AltQuickCOM 8457d705
Testnet has mining pool options now days:
https://solopool.com/,
https://btclab.dev/,
https://blockbuilder.app/stats - and a few others that I cant recall off the top of my head. When I joined Bitcoin many moons ago, there was zero pools for n00bs to test in.
Solopool just hit their first big boy Bitcoin block!

Also, we are US-based.

<3
Good luck, and please let me know if I can help from our end!!!