The first thing you need to do is decide how serious you are about upgrading your speakers. Klipsch rates the R820F sensitivity as 97db/watt. I checked a couple of less expensive Focal towers - they are rated around 91db. Sensitivity rating are subject to some fudging, but 6db difference = 4x the power required. Many speakers are listed below 90db/watt.
If you want to upgrade your speakers, you should keep that in mind when looking for an amp. If you're happy with the sound you were getting, then compatibility with the Klipschs comes first.
Did you get to hear them with your tube amps while still working fine? Did you feel like you needed more power, or had it to spare? If all was good (enough), you should consider another tube amp, or a modestly powered SS amp from a reputable company. If you want the option to change out speakers without having to revisit the amp, SS is far more versatile.
Personally, I think regular SS is still a better buy on Sound Quality/$ than class D. Also, on the Hypex amps I checked out, the power ratings were all for peak power - their RMS ratings were only 1/5 of that. Conventional amps are rated for RMS power. This makes them tricky to compare numerically.
I feel like a broken record sometimes, but there's a lot of love here on the left coast for Parasound, an SF-based company with a comprehensive line of well-designed & versatile amplification components. The NewClassic 275 v.2 gives 90 watts/channel for $900 list new, the 2125 model is 150 watts @ $1100, and the 2250 is 275 watts for $1800. If you get more serious, they have another line (Halo); their top amp is the mono JC1+ at over $9000/side. The design team is headed up by audio legend John Curl.