I think most often people use either a receiver or integrated amplifier with a subwoofer output. If it is an AV receiver then there is usually built in DSP to add a high-pass filter to the speaker outputs and perform room correction. This means any analog signal you feed to the AVR is being converted to digital and then back to analog. There is nothing inherently wrong with this extra ADC/DAC stage and it is probably inaudible. But if you feel better you can bypass this stage by feeding the AVR a digital signal. Or you could get a stereo receiver or integrated amplifier that has a subwoofer output but lacks DSP. They won't perform room correction or cut bass frequencies to your main speakers but they are an easy way to power speakers and control a sub. Usually these kinds of devices are large class AB designs, and although there haven't been many tested here, the ones that have are quite mediocre. The large companies that produce these kinds of products don't seem to put a lot of effort into making high performance products. Most of what they sell is just made to check boxes on a feature list at a given price-point with little attention paid to objective performance.
The reason I recommend DSP is because it will allow you to properly set a low-pass filter for the sub, a high-pass filter for the Elac UB5's, and perform room correction on the low frequencies. The bass quality of a system is the largest determining factor of sound quality for most people. It is quite possible that your UB5's sound shouty in the upper mids because your system is actually lacking bass, and when you turn up the volume to get good bass volume the upper mids are too loud in comparison. If you use a high-pass filter on the UB5's their woofers will no longer be asked to play bass frequencies and can perform mid range duty with lower distortion. The Subwoofer can obviously do a much better job of producing the low bass frequencies but the room will cause peaks and dips in the bass response that makes it uneven and less satisfying. That is why room correction is almost a must have for good bass performance in a room.
With DSP being such a powerful tool, it can also be quite complicated and difficult to do right. Many people will recommend using a calibrated microphone such as a
MiniDSP UMIK-1 or
Dayton Audio UMM-6 with the free software
Room Equalization Wizard (REW). This takes some learning and the first few times you try to use it probably won't result in the best possible outcome. However once you have learned how to take measurements and make room correction filters well it is very satisfying. With this kind of manual room correction you can use either software or hardware to modify the signal being sent to your speakers. The miniDSP 2x4 HD is a relatively inexpensive and effective piece of hardware for this task. Unfortunately it does not measure excellently well, and I can understand why you wouldn't want to "downgrade" to it from your Modi 3. On the other hand the DSP it brings to the table will improve your system far more then it's lackluster DAC performance degrades it.
An AVR gives you basic DSP power with easy to use automated room correction. But yeah they are big, ugly, expensive, have unnecessary features, objectively poor performance, and their automated room correction usually sucks. Good automated room correction is probably the best option for you though, since it doesn't have the learning curve of using software like REW. A product I use mostly just for its room correction is the
Paradigm PW Link. I picked it up for around $150 and just use its optical input and output. It comes with a usb microphone for use with ARC Genesis room correction software to quickly and easily improve your sound. You could feed it an optical signal, use the optical output to feed your Modi 3 which would connect directly to your speaker amp, and use the analog output of the PW Link to feed signal to a sub. The downsides are that there would be no high-pass filter on the UB5's and you would have to use the buttons on the PW Link or software for volume control. You could also get the Paradigm PW Amp which has the same room correction but also has a dedicated subwoofer output meaning it will high-pass filter the speaker outputs. It only has a low power amplifier though and will add an extra ADC/DAC stage.
As far as pro equipment goes, I don't know a lot about it but I have seen the Behringer Ultracurve Pro DEQ2496 recommended for automated room correction.