Looking for an integrated tube amp under $2500

The OP did not provide information regarding the size of the room in which the amp and speakers will be installed, or about listening habits and preferences.  

From a need for a solution that is no more than 7 inches high, can we deduce that space is limited ?   This may be important due to sensitivity of the speakers.  88db in a large room with a modest tube amp may not be enough power, but in a small(er) room may be sufficient.

Many good suggestions were made.   My suggestion is a bit out of the box:  Go vintage.

There are several models of vintage integrated amps, that once correctly restored, will rival the sound of new amps, at a comparable (or lower) price.  Vintage amps tend to hold value much better than new.

Sherwood 5ooo series amps are extremely well regarded, and sound wonderful.  Sherwood embraced a slimline design, and all power tubes are installed at a nearly horizontal angle, minimizing the height of the unit.

Fisher X202 is an outstanding amplifier, but will take up more space than a Sherwood.

Fisher X1000 is one of the best integrated amps from the golden age.  40wpc of EL34 power and an excellent preamp section.

Sansui AU series, and Luxman SQ series should be considered. 

One can find examples of all of the above for less than $1000 and then budget another $500-$1000 for careful restoration.

In all cases I would recommend inclusion of a quiet fan behind the amp due to possible ventilation compromises inherent in tight rack spaces.

Go online and look at the Audio Nirvana EL34SE. It’s 7 1/4 “ tall, comes only in Black,
runs fairly cool due to it’s oversized transformers, sounds AWESOME, and costs only
$ 999.00. Easy return if it doesn’t meet your needs.

Although I cannot do a comparison I can say that I'm very much pleased with the Rogue Pharaoh I purchased one year ago. It's a great unit IMO. Customer service by Rogue has been superb when I had any type of question or concern. Plenty of power to drive most speakers easily. Very nice phono stage. Only thing I changed, I did replace the original tubes with some NOS Mullard s. I'm aware it's not the ultimate but it does quite nicely in my listening room.

I actually had a Rogue Cronus magnum with kt -120 tubes which I really liked but it didn’t control the bass, was to loose. Went to the Hegel h100 which I liked but didn’t have enough power so I bought a h300. I then bought a new pair of large Ushers and needed more power so I went with a new McIntosh preamp and ps audio bhk amp.

This hobby can be a vicious cycle. Component synergy is a must.

Looking forward to having my CMII upgraded to the III, mostly for the lower noise floor. 

For a very smooth treble with great bass, swap the preamp tube for an RCA 5814 triple-mica black plate.