I used to be a "Flea" slapper as well; when I played on a 4 string. and when I first started playing Basss. RHCP was one of my favorite bands back in those days. I always thought BSSM was a brilliant album and very fun to play along to.
two things I think may help.
1) Consider it a 'Technique' that you can put in your tool kit. there is nothing 'wrong' with the thumbs down ala Flea for slapping as it lends itself well for fast popping runs IMO/IME. and fwiw you can still use it; just not for the double thumb stuff. so for example...you have your classic bassist "fingers" technique, there is your typical two-finger technique and you can transition to learning three and four-finger technique to the same end. (for four finger plucking I use I M R Thumb)
2) what ultimately helped me with the switch was more of a muting facility. when I switched to 5 string the spacing was tighter and there was one more string to mute as well. I had to make a few adjustments to my playing and guitar position as well. I used to sling hip low with my old Fender-P, but the ESP I found riding up near my chest lol.. but this was a result of a) trying to maintain a standing/seated balance and b) the neck was larger than my 4 string so I needed to adjust for comfort factors too.
anyhow, I found it easier to to palm mute and I also learned the floating thumb as a result of needing to mute that B-string mostly (and not just use it as a thumb rest) but back to the tighter string spacing: the overhand (Flea-Thump) was getting sloppy on anything other than the B string. so I started to move my thumb out like hitch hiker and strike the strings more parallel rather than perpendicular.. then I kind of stumbled into the double thump thing with out really knowing what it was called. my weird thumb is rather straight from the last knuckle to the tip, where as most people I know have a significant curve.. so I would flick it up and down sometimes like a pick of sorts.. Later to find out about the double thumb thing ala Wooten I started to refine my technique a bit to emulate him more: He has a much more physical attack than what I use.. I dont pluck out as much as he does, mine is more of an upstroke with my nail.. Vic really digs in.
anyhow. its a tool for the toolbelt. practice it slow to start and while you play the songs and scales you know well so its not too much brain work.. give it a go, and feel out its new comforts or lack thereof..
set it to the click once you get comfortable with it and then make it musical...
Good luck boss, Stay Low.