I expect the damping (not the springs) are too soft. You may be able to fit an adjustable seat and damping coilover to the existing atv attachments. Remove one side, raise the axle to the full bump position, then measure the distance between the mount eye centers on the axle and chassis. Short enough is more critical than length. Worst case, the attachments can be altered for a longer compressed length coilover. If the atv springs won't fit the new coilover, measure the atv spring rate using a bath scale and a press to squeeze it down at least an inch or measure the spring and do the math. Seat adjustment and distance at full bump will help determine the new spring off-the-shelf length.
I'd also check the condition (loose and/or soft?) of the link ends. You can fit a camera under the car to record wheel movement on hard accel to see how much the link attachments allow the axle to oscillate.
It looks like a good, parallel, equal length links that are level at ride height with bushing links on a fixed axle attachment (versus a "birdcage"). For more anti-squat/traction options, I'd consider reworking the chassis upper link attachment plates with multiple holes for a shorter upper link and a slightly lower mounting hole option, keeping the lower links level at ride height and as long as possible. Also making new links that are adjustable length and spherical ends with room for clearance spacers on each side of the spherical (may need to adjust distance between double shear bracket flanges).
_________________
Miata UBJ: ES-2074R('70s maz pickup)
Ford IFS
viewtopic.php?f=5&t=13225&p=134742Simple Spring select
viewtopic.php?f=5&t=11815LxWxHt
360LA 442E: 134.5x46x15
Lotus7:115x39x7.25
Tiger Avon:114x40x13.3-12.6
Champion/Book:114x42x11
Gibbs/Haynes:122x42x14
VoDou:113x44x14
McSorley 442:122x46x14
Collins 241:127x46x12