As a fellow system administrator, web administrator, and fellow forum user, I have often found myself settling on WoltLab Burning Board
They do have a full working importer for phpBB 3.2 (as well as all previous phpBB versions). The software is fully responsive, which means it fully supports desktop and mobile device sized screens, which I believe is important, especially on a support forum as most people seeking help are likely using a mobile device when their computer is offline (down). Most importantly, the software is very good at keeping general spam out (which I know is your concern) and also offers several 3rd independent modifications to expand on the core to that end.
While WoltLab Burning Board is not free, it is the more affordable alternative as the bottom line price is the lowest (90) and there are no subscription fees (you buy it, you keep it, and continue to get updates for it). For example, if you bought v4.0, you ended up with nearly 5 years (1/2 a decade) of free updates and free supports.
A side note, if you do decide you like WoltLab Burning Board, I would be willing to contribute to the funding so you can obtain it. As an open source project, you have already given to the online community at large and I do not mind playing it forward by helping if I can.
Alternatively, if you really are looking to stick with free forum software, I would suggest either Flarum
. The downside to Flarum is they are still in development and for that reason, while they do show promise, the software is not fully 100% ready for prime-time (in my opinion). NodeBB would be a good alternative as they offer both free and paid support, although the software is not as simple to always upgrade or backup (I make system images regularly for this reason).