I suspect as is the human way there will be a lot of hand wringing that 'something has to be done' (why do I always think of Helen Lovejoy from the Simpsons when I type that), before people sit down and think about it and realise that to keep what seems to make the National popular not a great deal can be done about it.
Taking a few points....
most of the carnage (bar the first fence) was caused by unseated horses running riot.
Short of having snipers dotted about the course I honestly have no idea how this can be managed (bar stopping the race to clear them but that's going to defeat the point of the race), (the following is not aimed at you but in response to an 'idea' that seems to be rife on SM) the idea that someone can just catch a loose horse is I assume only being perpetuated by people who have never had 1/2 ton of horse with the only thing on its mind being not getting caught and running with the herd bearing down on them, it ain't gonna happen and probably has more scope for injury than the present situation.
TBH what was probably more worrying on Saturday was the number of horses that got off the course and were running about on the in field bits with Ambulances and TV cars running about in there as well god only knows what could have happened.
I feel similar to Berni in that the bigger races with over twenty horses probably do need something done about it or adapted. One way might be to have four heats of ten horses, with the top three racers going through to the final. Instead of having forty horses all racing, they'd be ranked on form and put into said four groups/heats. In the Grand National Final, it would be between the twelve best horses from each heat. Also from a bookies perspective they'd have more races to offer the punter to bet on and from a horse owners point of view they would be in with a greater chance of being able to win the national.
Reducing the numbers is the obvious solution, but would, I suspect, get rid one one of the main draws of the race for the average man in the street, that its pretty much a lottery and with a big field you get big odds so the pin stickers have a decent chance to win big on small bets (our daughter won a fiver off a 25p each way bet on Saturday!) get the fields down to 20 and the odds would all tighten right up, so if over several races possibly better for the bookies but little different to thousands of other races during the year, including existing ones at Aintree over the same fences.
A side note that doesn't necessarily impact welfare of the animals but I'd also ban race owners/trainers from having more than three horses in each race. It can't be right that the likes of Mullins, Henderson and Elliott can have around six horses in one race. There needs to be a fairer spread across the competitions rather than three trainers covering nearly half the field.
Good luck with that as it gets you into all manner of issues regarding constraints of trade etc, ultimately owners want best trainers for the best horses and outside the big trainers it a very hard business to make sustainable. Racing in the UK is dying on its arse a bit as the prize money isn't great, its why the BHA etc are terrified of any clamping down on the betting industry as without their sponsorship I suspect racing would barely last beyond point to points over here.
OTTOMH all I can possibly see them doing re Saturdays mess (not helped by the delays as you ended up with horses and jockeys considerably more wound up than usual bearing down on the first and in the desperation to get them off the start was a bit of a shambles) is possibly a field reduction to say 30-35 (whatever they think retains the character), and in terms of the opening fences either make the run to the first much longer to try to spread them out a bit (but might mean they just get faster and faster so could defeat the object or make the 1-3 fences physically wider and maybe lower to spread them across the course a bit and easier to jump.
No easy solutions and thankfully not down to me.