I have no experience with VAC but with my Octave V70se and now V110 I can say I have rolled a few tubes. But first when I say warmer I mean there is an emphasis in the lows and and a slight roll off in the highs. Linear is very well balanced from the lows through the mids and highs. My V70se came stock with SED KT88 winged C. Later I tried some GL KT88 re-issuse. Very similar but the SED's are a little warmer sounding where the GL's were slightly more linear. I also have the vintage Gec KT88's and they are very linear but a tad dry sounding. The EAT KT88 diamonds are excellent sounding if you like linear. But the EAT's come with a super premium window sticker. I found out the EAT's really don't last very long if the plate voltage is higher than 450V. The V70 has a plate voltage of 540V and I lost 3 of 6 in less than a month. Another tube that I like a lot is the Ei KT90 type2 (in the V110 now). Very linear and musical with a huge soundstage. Reminds me a lot of a great EL34 on steroids. It's a shame you shouldn't use 6550's because my favorite tube is the original Tung Sol 6550 solid black plate. It's a warmer sound with 'just to die for midrange'. The solid grey plate is close but a slightly more forward midrange. The last KT88 I also really like a lot is the vintage Tesla KT88 (NOT JJ). But it too is a tube that doesn't last with a plate voltage above 450V. Are KT120's an option? Honestly for me it is my least favorite tube but a lot of folks swear by them. Again to me they are extremely forward and punchy but just don't quite sound right to me when compared to others. But they are cheap.
Since my Octave integrated uses a single 12ax7 for an input and a pair of 12at7's for driver/inverter I can't comment on the 'little' tubes except all tubes will make a difference in sound.
Last I will say there is no bad sounding tube. Just ones that sound better than others. But if you have the wrong combos of little and big tubes it can sound pretty bad. Example to me the little Mullards are very warm sounding and sound pretty good with the KT120's they don't sound very good with the original TS 6550 black plate.