I keep forgetting about that processor, mostly because it only has balanced XLR outputs for left/right, but since you are only going to use RCA interconnects to your amp, it shouldn't matter to you. The Sigma SSP uses the same audio stages as the previous SSP-800 (which is a fully balanced design). The Sigma is only 3-3/4" high, which is excellent for you. However, the Sigma SSP also had two versions just like Krell Foundation. The original only supports HDMI 1.4 and 1080p. The newer "mkii" version will support HDMI 2.0 and 4K UHD and some limited Atmos decoding. Here's a "mkii" version for a little more at $2799:
https://www.audiogon.com/listings/lisa4f8g-classe-sigma-ssp-mkii-7-1-channel-home-theater-processor-...That being said, the Sigma SSP uses switching power supply for everything. Since your AVP-18 also uses switching power supply, it's probably not a big deal for you. The Sigma SSP will still be a significant upgrade from your AVP-18 in all areas.
I think the Krell Foundation will still have better sound quality. One of the things I really like about the Krell design approach is that they use linear power supplies for everything, including both digital control circuits and DAC VREF power supply. Most processors will use a linear power supply for analog sections, but still use switching power supply for digital sections. I think the Foundation is going to sound smoother, fully and more natural than the Sigma SSP, but it's going to be $1700 more, lol. The Sigma SSP will still be a huge improvement over your AVP-18, though. I guess it depends how much you really want to spend, lol.