the DHA VT1 Bassoverdrive will do very well what you expect, only is is not very small and needs an own PSA (which all real tube pedals will need anyway). the aguilar tonehammer will work well, too, but also needs 18V or PSA or phantom power through the DI.
the SFT is only an overdrive and doesn't work too well as a preamp. havent tried the dragon and the bb though.