Bike-packing the SDW is the only way to do it, in my opinion, it looks like a blast
I walked the SDW over Easter weekend (Winchester on Friday lunchtime, Eastbourne on Monday teatime) and found it to be a bit of a trudge with few highlights. There was a lot of time plodding through paddocks with monocrops and manure and that got tiresome; a bike would have made the tedious sections tolerable or even fast, tail-sliding fun. A bike would also make visiting the nearby-yet-off-trail villages a lot more appealing.
Sometimes the trail seemed to be routed for passive aggression, like when it departs from the Seven Sisters visitors centre to go up a hill and come back down, only to rejoin the path from the visitors centre that is much more direct and goes past salt-marsh, which is a tad more interesting than yet more sheep paddocks.
Overall, I'd give the SDW 3 out of 10 for a walker and would advise against doing it*, but I would take the chance to hit the trail again on two wheels.
Anyone doing it should be aware that Housedean Farm (mile 78) is right on the A27; the noise and pollution is simply incredible and I can't understand anyone staying there when aware of it. There's a decent wild camping alternative around mile 80 (closer to Eastbourne) between some gorse bushes.
*3/10 might seem harsh but the train journeys cost £72 and on the walk I spent a long time comparing the SDW to the Cairn Gorms, Southern France etc. which would have been just as easily reached.