I guess I would start with the KT66, they should drop in with a bias check. The EL34 will need some finagling of the power tube socket, screen resistors etc. Not a huge deal, but it seems like the 66 would be the easiest place to start....
I am assuming Ceriatones PT can handle the current demands of the new power tubes. I believe Nik uses the same PT for the X3 model, so you should be OK.
Good Luck

I like Wyatt's post here. it is very well done and is accurate with regard to tube amp theory. 

One thing that I found by a happy accident is that many modern build guitar amps use plate voltages that are above or at the maximum ratings for the power tubes.  A few amp builders are using power transformers that offer lower secondary (high voltage tap) voltages than what the majority use.   This is in regard to 6v6's and 6l6's.   There is a wonderfully different tone palette available by doing this.

I found this out purely by accident from purchasing a wonderful sounding amp through eBay, a Siegmund Midnight Blues (Blues Breaker) head.  It is offered from the builder tube rectified, also supplied with a proprietary SS rec adapter in three different voltage ratings for the main power transformer and also a choice of at least three different styles of output transformer in style of windings and capacity for current.  Mine was built with the lowest voltage PT option and has the larger, but not largest sized Radiospares type OT.  This type of OT was only used in the very few first Marshall amps due to its excessive cost.  Even when using only a pair of 6f6g's, the amp is surprisingly loud, and wonderful sounding. 

Being a vintage tube collector with literally hundreds of vintage preamp and power tubes in my stash, I found that I was able to run the older versions of 6v6 and particularly 6l6 power tubes, and the tones I got from doing that were jaw droppingly gorgeous.  Since the amp uses a fixed bias pot and bias balance pot in it's build, I was able to try tubes ranging in output from 6f6g all the way to 6550 in power tubes, and the output sockets had pins 1 and 8 connected to run el34's and kt66's as well.

My point here is that if a lower voltage PT is used, then the user gets to try the earlier versions of 6l6.  There is an increase in power over 6v6, but not as much as the jump in output to the later build 6l6gc types available today, and frankly the old glass just sounds better, in some cases MUCH better.  Currently I'm running a Bendix Red Bank 5r4 "tater masher" in the rec socket, and a pair of British vintage Emitron (Genelex type) kt66's in the power tube sockets, and the tones are beano-ish to say the least. 

So if this 5x3 were built with a PT having say, 275- 300v secondary taps and in sufficient current capacity, with all other things considered the use of these older 6l6 types, particularly the real 5881's, (Sovteks excluded) 6l6wgb mil stock, or 6l6gb's  should result in a wonderful sounding build.  Output will fall within the range that the OP wanted.  Old style tubes for an old style amp platform!  These older tubes are available on eBay for less than horribly expensive prices, and even though you might have to get  more than just a pair within a chosen type to put together a nicely balanced pair, the results are very much worth the effort.  And of course with pins 1 and 8 connected on the power tube sockets, this platform should be able to run kt66's or el34's as long as sufficient heater current is available from the PT.   Perhaps a few component values in the power section could be tweaked to optimize the circuit for el34's.