I've upgraded several good ADS speakers, incl. 780 2, 980 2 and 1590 2.
Here's the low hanging fruit I've found with them.
Better wiring will help and is not too difficult. > 14ga. on woofers is quite audible. OFC or better copper works good, smaller guage on mids and tweeters, of course.
i'd leave the crossovers alone. Replacing some or all parts will have unpredictable sonic results. It is possible lots of money and effort there on better parts may make sound worse overall.
The biggest improvement is damping all the cabinet walls. The woofers have a high crossover point so wide range cabinet talk is significant. It significantly muddies bass and the midrange too.
Sonic Barrier is an affordable good product, and not too hard to install:
https://www.parts-express.com/Sonic-Barrier-3-4-3-Layer-Damping-Material-w-PSA-18-x-24-260-530?quantity=1Remove about a third of the fiberglass stuffing if you do this so you don't overdamp the cabinet.
Woofers are firmly attached, and prying them out with a screwdriver or the like will likely damage the wood. Use a sheet rock or sheet metal screw that is screwed into the woofer basket mounting hole (not into the cabinet), then grab the screw head with pliers and give a sharp tug. It may take several tugs to get the woofer free.
The wiring and cabinet damping will significantly improve ADS speakers.