Yes I'm pretty much asking just that. If Binance is just requiring you submit the docs and images I would just photoshop something, I dont need to steal someones identity just need to be in binance long enough to convert the coins and send them to myself. I just did a trial with Bitfinex and that worked, need to figure out how to convert the coins there and send to my CB account.
It's riskier if you will do it with Photoshop. Someone close or related to you can do that verification but there might be a chance that they will look at your used IPs. Already consider contacting the support on that matter? As you said, you just follow the instructions but got that service error on the way. They might allow you to push for your withdrawal using your real IDs as your account isn't that active within the timeframe they discontinue their service in your area.
It will be a tough decision on your part but as you have mentioned, you already did that crap on Bitfinex so you now have experience dealing with that situation.
Anyhow, there's no other way so need to decide for yourself. In the first place, you already accept the risks and prepared to kiss your money goodbye if the process will fail.
