50^9 / 2^4 / (134 000 * 2.99) / 3600 / 24 = 3526.3 days
Yes, but i find 16 times reduction (since 12 words seed has 4 bit checksum) worth mentioning. And looking at btcrecover, 100K/s seems to be low approximation since Nvidia 1660 Ti have 134K/s[1]. And since service like vast.ai only offer high end GPU such as RTX 3080 Ti (which is 299% faster than 1660 Ti), the search time should be lower.
3526.3 * 24 * 0.301 = $25473.99
On vast.ai, cost of single RTX 3080 Ti is $0.301/hour and it costs about $25473.99. So it should be viable if OP roughly have more than 0.5 BTC. Take note that,
1. Additional benchmark is needed since it's just theoretical number.
2. Since vast.ai also offer decent CPU, you could use it for small boost.
3. Assuming 50 words chosen by OP is correct.
[1]
https://btcrecover.readthedocs.io/en/latest/GPU_Acceleration/#performance-notes[2]
https://www.techpowerup.com/gpu-specs/geforce-gtx-1660-ti.c3364[3]
https://vast.ai/console/create/, instance ID 3279060
A better GPU is not necessarily going to result in more efficient searching because of CPU bottlenecking.
Due to the large investment required to find the seed the OP is looking for, I am hesitant to recommend he pursue this (even while overlooking the security issues) due to the risk that the OP made a mistake regarding the list of remaining words.
Regarding the security issue specifically. It does not appear vast.ai is targeting crypto users, and their target market appears to be those wishing to train machine learning models. This means the host is unlikely to be watching and waiting for you to find a private key/seed. So you should have time to move any coin that can be spent using the private keys derived by the seed. With that being said, using any cloud computing service to find a seed means your seed has been on a computer that was exposed to the internet, more specifically on a computer you do not have full control over. It would be best to move any coin to an address derived from a freshly generated seed if you can bruteforce the seed.