@cluster, I've had good results even with low spec subwoofers, when integrated with WiiM subwoofer management and tamed by RoomFit. This includes subjective listening experience as well as objective measurements.
I cannot say anything about the T5s and personally I would rather look for a sub with no integrated DSP functions. A DSP is not needed with any WiiM amplifier and the little money available should rather be spent on more fundamental things.
There's nothing wrong with tweaking and tuning a budget sub. This includes (partly) stuffing any existing vents, of course. Just don't make anybody believe you that closing the vent on a ported sub always makes it "better". That's simply not the case.
Also don't even think about connecting a sub "the REL way" by connecting the amplifier's speaker outputs to high level inputs of the sub. This is vastly inferior to using the sub out. When using WiiM's subwoofer management, the main speakers are relieved from outputting bass below the crossover frequency. For the mid-woofer in your Diamond 220s this means less heat, less cone excursion and thus less distortion. Should you feel that there is too little bass output, this can be fixed by proper setup of the crossover frequency, the phase switch, latency sync, sub level, RoomFit and finally custom EQ. You'll be getting tons of support on these issues in this forum.
If you happen to live in the UK and can afford something like the BK Electronics P10-150-GEM, that would be a good option.
bkelectronics.co.uk
You might be able to pick up a second hand unit of its predecessor, the Gemini or Gemini II:
The availability of budget subs differs quite a bit depending on where you live on this planet, so I won't mention further products for now. But the bottom line is that even a cheap sub when set up correctly and maybe tweaked a little bit can usually improve the sound of small bookshelf speakers in your room.