used Integrated tube amp under $1500 for Klipsch Cornwall III's?

With Forte IIIs you can use anything from low wattage to whatever...If I didn't already own have a Dennis Had "Inspire Firebottle" single ended amp I'd seriously consider the Coincident Dynamo (nearly did when considering the Had amp, but was charmed by Had himself in a video, and the Firebottle was cheaper as a barely used 12wpc model). With a Schiit Freya this makes a combo that's hard to beat by any integrated...for something in the push-pull tube world I'd look at the new "Black Ice" stuff from re-named Jolida MD, as having owned a 502p amp I can vouch for their quality, and they're still relative bargains compared to other stuff out there.

Look at used Cary Audio. Built well and excellent sound on their F1 mods or upgraded caps, Hexfreds, etc. There’s no need for complicated thoughts. Something that can be worked on and preferably from a company that’s still around like Cary Audio or Conrad Johnson.

That Harmon Kardon TRIO 224 sounded intriguing, I found this

https://forum.polkaudio.com/discussion/105874/harman-kardon-trio

I came across another TRIO the other day, different manufacturer. They never mention 'pre-amp', but they show phono inputs, but they don't mention if phono eq and/or tape head eq exists. 

HK 224 was new in 1958. Tape was stereo in 1956. LP stereo in 1958, soooo ...

The HK has a switch on the back, I suspect it is one set of low level inputs, and the switch sends that input to either an internal phono eq, or to a tape head eq circuit, then on to the amp.  I want hard facts.

In any case, it is 12 wpc stereo, or 24wpc mono. I suggest you start your tube adventure with 30 wpc, so you can change to different speakers in the future.