Yeah, spoofing the FW version should let you sign in, activate and everything else you can do in the Store bubble. The only thing that comes to mind would be that your Vita maybe has already downloaded the update, which in turn asks you to update it everytime you try to sign in and/or go online, so you should delete the update file, found in either 'udo: PSP2UPDATE/' and in 'ux0:bgdl/' and see if that solves your issue.
What game are you trying to play online? (Soul Sacrifice Delta is the one that comes to mind if it doesn't let you go online to play).
Because there's literally no difference between actual firmware functionalities currently? The talk about "more stability" in 3.60 is just fan-fiction as technically every "must-have" plugin used (and still maintained) by the community works in the 4 latest exploitable firmwares, 3.60/3.65/3.67/3.68. And a lot of people can prove that, me included. Having to open a bubble, which takes a second to do, doesn't affect nor hinder the exploit's functionality.
Yeah, yeah, we know Enso is the "preferred FW because of permanent hack", but that's it. Not having Enso doesn't mean the plugins will fail or cause issues.