Well Hostgator isn't exactly a great hosting company with its endless list of limitations for shared hosting. If you have quite some visitors already then all the bots will only make it worse, have you ever considered moving to a VPS? A VPS will give you more flexibility and a lot more resources.
By looking at the access log you posted, it looks like they attempt to create accounts. The problem is that such bots don't respect robots.txt files and banning their user agent is not going to work out because it uses different user agents.
Do you have any anti-spam/bot plugins installed already?
Also
https://vborg.vbsupport.ru/forumdisplay.php?f=30 is the section where you can request paid services.