PIE. *(s)per- (e-grade) **(s)per-eH-? (e-grade + e-grade laryngeal)
PIE. *(s)pr̥- (Ø-grade)
PG. *spurą sb. "trail, track"
PG. *spurjaną vb. "to pursue, track"
PIE. *(s)pr-e-g- (Ø-grade, g-extension)
PG. *sprekaną vb. "to speak"
sprak vb. "to speak, talk"
PG. **sprakōną vb. "to emit a noise"
sprak vb. "to emit sparks; to crackle, rustle"
PG. *sprekalą sb. "freckle"
sprekl sb. "fleck, spot"
PG. *frekalą sb. "freckle"
PG. **frekan- sb. "freckle"
frekno sb. "freckle"
frekno ad. "freckly, freckled"
PG. *frekaz ad. "greedy; vigorous, capable"
PG. *sprēkō? sb. "language"
sprák sb. "language"
PG. *frōknaz? ad. "strong, bold"
PIE. *(s)pr-e-n-g- (Ø-grade, n-infix, g-extension)
PG. *frankaz ad. "courageous; free"
PIE. *(s)pr-e-n-ǵʰ- (Ø-grade, n-infix, ǵʰ-extension)
PG. *springaną (*spreng-) vb. "to run, leap"
PG. *sprangijaną vb. "to make run, leap"
spreng vb. "to explode, burst"
PIE. *(s)pr-e-n-d- (Ø-grade, n-infix, d-extension)
PG. *sprintaną (*sprent-) vb. "to jump"
spritt vb. "to burst, blossom; to rush, leap"
spritt ad. "pure, genuine; utterly, fully"
PG. *sprantijaną vb. "to make jump"
sprett vb. "to make jump; to flick open"
PIE. *(s)pr-e-w- (Ø-grade, w-extension)
PG. *spreutaną vb. "to spurt, gush"
PG. *sprutą sb. "sprout, offshoot"
PIE. *(s)per-
PIE. *(s)per-?
AGk. sphaira? sb. "ball, sphere"
AGk. speirein vb. "to scatter; to strew"
AGk. aspairein vb. "to quiver, fidget"
PIE. *(s)per-k-?
AGk. sperxein vb. "to urge; to pursue"
AGk. sperxnos ad. "quick, swift"
PIE. *(s)per-g-?
AGk. spargan vb. "to teem, be bursting with"
Lat. aspergō v. "to sprinkle, splatter"
Lat. dispergō v. "to scatter"
Lat. spargō v. "to strew, sprinkle; to scatter"
PIE. *(s)per-m-?
AGk. sperma sb. "seed"
I really don't see a problem.
All ultimately derived from PIE. root *(s)per- (Pok. 992) with various extensions and different grades, although some of the recent reconstructions are new to me (Köbler might also be a little less conservative with his reconstructions). Still, the basic semantic field seems to be of something forcefully moved or the result thereof, which not surprisingly seems to fit most reflexes fairly well.
All the while avoiding any unnecessary new speculations.