If you have already purchased the
Speed Paints, then, yes, strip and start over with a proper base coat compatible with
Speed Paints.
If you have not purchased
Speed Paints yet, I would suggest using
Acrylic Paint Pens (average of $0.42 per pen!), followed by a dark wash. Give me a chance before you click away...

I've been doing assembly line painting since 1995: I organize figures by grouping them by pose, then applying the same color, same brush stroke, on each successive figure. I got my painting time down to 10 minutes, per figure, on average. That includes batch priming, block color application, and
Dip'ing (brusing it on, not dunking it in the can) with removing the excess urethane stain back into the can using my throw-away school painting brush. Example:
Gnome Spearmen, approximately 20mm tall each;
Human Ultra-Heavy Cavalry (BattleMasters game plastic figures).
Recently, I tried using inexpensive
Acrylic Paint Pens with a Brush Tip (the other sorts of tips really do not work for miniature painting). Using these in place of paint bottles and a palette, I cut my figure painting time down to 5 minutes per figure! Some
Chaos Archers (BattleMasters game plastic figures; EM4
Dwarven Halberdiers converted from Spearmen to hold the
metal Halberds.
Speed Paints will yield better paint quality results, for roughly the same amount of painting time, but they will cost considerably more than a set of Acrylic Paint Pens (
$0.69/pen color:
72 colors will cost you around
$50, versus 89
Speed Paints colors for
$507.59 + s/h, or $5.70/color, w/o shipping factored in). That $450 you saved on paint, will buy a few new armies worth of figures...
In case I did not make it clear, the
Speed Paints will average around 5 minutes painting time, per figure, so the same speed as what I achieve with Acrylic Paint Pens and
The Dip Technique (I batch them for a matte clear coat after the urethane stain dries, which is included in my time evaluations for average total painting time per figure --
drying time is not included in my calculations, but I bake them in a dedicated slow cooker, at 200 F for 30 minutes, after
Dip'ing them, before I matte clear coat them).
My point in posting, is that you have other options than just
Speed Paints.
It depends upon what you are painting for: the 2% of the time in which you view your figures two inches from your orbits (eyes), or the 98% of the viewing time when they are sitting atop your gaming table? It is a matter of personal choice. I paint for the
98 percentile, ignoring the 2%. I am all about speed painting my figures as fast as possible, without spending loads of money on paint. The Acrylic Paint Pens cut my painting time in half, with virtually identical results to what I achieved without them. Up to you. Cheers!