FWIW, VH Audio also has some oil caps too.
Those teflon V-Caps do sound intriguing. AudioCap has teflon/tin foil caps as well. Same manufacturer as the MultiCaps I recommended. These caps are the creations of one Richard Marsh(the founder of Marsh Sound Design). If you know how good his electronics are: now you know part of the reason. One nice thing about tube gear- There aren't that many devices in the signal path(not really much to replace). Oh- the V-Caps take about 4 or 500 hrs to fully burn-in(so they say).
I have the BAT VKD5SE with SuperPak and the VK50SE. I have never found the BAT house sound to be "tubey". I think in many cases it can be a simple matter of tweaking power cords and cabling. The BAT tube gear has always provided me with a sense of air and presence that tubes do well, yet solid bass that is more like solid state.
In my experience, the power cord can often times take care of this type of "bloom". Sometimes too much of a good thing can lead to a bad thing and that may very well be the situation with your matching of components and cables. Since cables are rather inexpensive compared to components, I would recommend changing up some power cables or interconnects first. I have found the different Elrod power cables to be excellent for tubed front end gear. It would be good to know a little more about the entire setup including cabling to further look at the situation.