Well... your best bet is to find some company that offers something like that.
EAC is dead for 1.6 because their servers are shut down for 1.6 but you can still play with the client... if you made your own software that just launched EAC and made sure that the users have the client running it would be the most reasonable achievable outcome for you. But you're a bit unlucky because there are quite a few EAC bypasses in the public for 1.6, so it would be useless for someone who wanted to cheat, even an average skid would be able to bypass. Even then you would still need to gather system information to assign it to a STEAM_ID and even then you'd need to find a way to see that a user isn't already banned from EAC on 1.6 or if the system info matches to a banned steam id, + they could just open it and let it hang at the 'you are banned' error pop-up and play safely on your server, or use basic free spoofers to bypass your stuff assigned to the banned steam_id
It would be easily bypassable by someone who knows and cares enough (average to even beginner reversers, or the correct skid with the correct free tools) + you would have to make sure that the player actually connects from THAT pc, you would need to know which pc is the actual player on the server in case some1 has two pc's and connects from the one that isn't running the ac.
Even if you get an actual dev to code it for you it's gonna take a lot of time and especially MONEY, and don't forget that AC's are never a solution forever, and not all AC's are equal, so you'll have to get a damn good coder who knows what he's doing - and those cost a LOOOOOOOT... my guy is it really worth it? Then if a game update happens or a cheater bypasses ur stuff then you have to pay the coder to investigate and update, and again you're paying him to maintain that project - it's never gonna end. Just install some demo scanners on your VPS and some other plugin solutions that would prevent the cheats from reading if entities are alive or dead, will stop all kinds of drawing except sound esp, and all kinds of triggerbots and aimbots there are a ton of autobhop knifebot detection solutions, some modules like resource checker, reaimdetector blablabla a lot of free stuff.
And on top of ALL of this, you'll also have to convince random players that try to join your server and getting kicked to download a random anticheat they never heard about before, good luck! It's basically a death sentence for any server especially nowadays.
You can also do your own plugin and see if the client has cheat cmds that return values by using query_client_cvar, 99% of cheats are outdated/or have some sort of custom cmd so you could easily find other ways to crash those clients/ban them if their cheat cmds return values.
With the modules + plugins you'd stop about 99% of the cheaters, the rest .99% with the demo checker stuff and maybe third parties like wargods and the rest .01% you'd have to manually ban. The EAC idea wouldn't be bad either, but then again... public bypasses and you'd still need your own client + server and maintaining both of them.