Good call from Whiteram, the Trilogy Suite would be a beefy stratalternative for a P90. I don't know the Lundgren.
The Slowhand is smooth with serious mids and the Holy Diver provides thick rock- and metaltones.
If you want to go a tad more vintage you could think of Abraxas, Slowhand, Slowhand too. The Abraxas does Satriani-stuff very well, but has enough PAF-pedigree to give you classic rocktones too. Or Abraxas, 59 slabboard and Slowhand for ultimate versality.
Alternative could be the Crawler, I have this one in a swampash-strat and is beefy, warm and growling with some gain, leadtones are thick with the right amount of compression for soloing, also above the 12th-fret. Topend is round, but has enough bite, don't worry. In the bass the Crawler is little more loose then the HD, but still tight enough for me. Has more PAF-dna then the HD. This one cleans up great and splits very well with the middlepickup.
If you like P90's you could also check out the Stockholm for the bridge.
Btw, I have the VHII in an Fender American Series ash-strat and it seriously rocks. Splits well, but not to the degree a Crawler or HD would. The higher dc-resistance make them perfect for a balanced split.