Whenever I notice a tendency to go sharp, it is (in my case, I emphasize) ALWAYS because I'm using too much pressure on the mouthpiece. This is a particular danger if you are trying to increase your high range.
Over the past several years I've played alongside a number of decent to very good tuba players in community bands. Exactly three of them have exhibited good tuning and intonation. Several of the others had terrible difficulty tuning their horns to 440 and habitually play with their tuning slides pulled out 3" or more. These guys have very good technique, but in hot weather (~ 85+ deg F) they CANNOT get their instruments in tune. Yet these are high quality instruments (typically Miraphones) and they use standard mouthpieces on them (e.g., Conn 120S, Schilke 66 or 67, or reasonable Miraphone ones). When they tune in a band practice session, they are always sharp, pull their slides more, and still have trouble. Some of them are very experienced and at least a couple used to be in military bands. I STRONGLY suspect that they are just using too tight an embouchure and/or too much pressure on the mouthpiece. This is very easy to do if you don't think about it and work at correcting it.
Something similar MAY be your problem. If you don't feel that you "have a lot of control over the top lip", and if your corners are "anchored", then that MAY be because you have the mouthpiece firmly mashed (good Southern term I've learned) up against your top lip.
Just something to check. Try some exercises where you attempt to use the least mouthpiece pressure you can in playing all the notes, and see how that affects your tuning and intonation.
Gary Merrill
Wessex EEb Bass tuba (DW 3XL or 2XL)
Mack Brass Compensating Euph (DE N106, Euph J, J9 euph)
Amati Oval Euph (DE 104, Euph J, J6 euph)
1924 Buescher 3-valve Eb tuba (with std US receiver), Kelly 25
Schiller American Heritage 7B clone bass trombone (DE LB K/K10/112/14 Lexan, Brass Ark MV50R)
1947 Olds "Standard" trombone (Olds #3)