All I can say Heikki, is measure the new internal dimensions imposed by the internal slide (when bell note is in-tune) and work-out the average of the new bore, then go to the flute-o-mat and find out how this new dimension will affect the positioning of the tone-holes.
On top of that, (without doing any math) I would intuit that you have effectively made the bore reverse-conical which would probably accentuate the cylidrical tendancy to go flat on the second register - OK for reeds, not OK for fipples as fipples have the added physics of the ambient air-pressure and the energy balance that affects the tube-shift caused by air forcing the resonant tube to displace towards the bell.
A solution might be to rebate the space that the slide will occupy (hence not changing the intial conditions very much) - which will minimise the bore volume change as you tune down (or up). Some kind of enlarging-drum might be emplyed on PVC to sand-out the rebate - make sure you have an adequate filter to not breathe the fumes and dust! Perhaps a cylindrical bit of wood might be made with a longitudinal slot to hold a strip of sandpaper (whose additional circumference has been calculated) - perhaps also, with a short taper to lead it in (the sand paper will conform to the contour under pressure of drilling) - attach it to a sanding disk mandrel with the disk removed and a long bolt through the centre of the wooden drum - attach to a hand-drill chuck - insert and enlarge (largely self-centering). Otherwise, get an appropriate internal-diameter cutting tool and do it on a lathe.
Keep in mind that tuning slides are very aproximate in their affect - the proportionate change in tone-hole position is not achieved through a tuning slide and inaccuracies will occur as the slide is moved.
Once again - do the math, use the flute-o-mat and get to understand the non-linear relationship between bore and tone-hole positioning. How those guys got to encode how much finger fills a tone-hole I will never understand - it could be a catenary but the real world would dissagree nine times out of ten!
Now you have a disembodied head, you are licensed to play-around with bodies <snigger>
Above all - have fun!
