So, I have a few thoughts here:
(1) I feel what you're saying on limiting discounts, though to be honest I've found the mounting pricing differences in the airline industry to be dizzying almost to the point that I get nauseous. My concern would be that Amtrak would be more likely to clumsily price itself out of the last-minute business entirely. Also, having at least some sense of what the price range is going to be (e.g. that a last-minute roomette isn't going to randomly run $1000 to Florida because the computer got possessed) is advantageous. The problem is that when you refer to the problem of limiting discounts, if you /don't/ limit them then you de facto squeeze out last-minute flexibility. Then again, I've avoided "saver" fares and their previous incarnations because they are frequently not upgradable (and I've often got more upgrade cards than I know what to do with).
(2) I suspect that a lot of the "record ridership" is due to increasing short-to-mid-haul rider counts (and, of course, to packing a number of less-utilized state and corridor trains more crowded). The fact that several states /did/ get slugs of new cars in the late 1990s/early 2000s (and that the Acelas allowed some equipment to cascade elsewhere) didn't hurt...and of course, you've had VA extending several Regionals from WAS to Roanoke, Norfolk, and Richmond, which has packed a few hundred thousand more riders into the mix.
(3) On the NEC in particular, I really have to come back around and wonder if it wouldn't make sense to add some sort of "commuter class" service with a semi-fixed fare (probably a peak and an off-peak fare, or something similar). You could easily find a fare level that's modestly above what the commuter services charge but also below non-discounted standard coach fares. I also know that a few of us have mused about whether it would make sense for Amtrak to grab a few sets of NJT/MARC-style bilevels or other commuter equipment, add on a "standing buffet" in UK terms (e.g. it would sell food but you'd have to go back to your car) and run some "all the stops" trains with tickets at a discount. An extra 15-30 minutes' travel time for an unreserved seat on a high-density train for a guaranteed end-to-end $49/69 fare (note that covering the relevant portions of the Corridor on commuter tickets would run $38 and still leave you with a gap between somewhere in Delaware and Perryville, MD).
#3 is rather painful to me to think about, but I have to wonder if the trade in at least some class of service wouldn't be worth it in terms of adding ridership at more affordable prices without setting Congress's blasters to "whine". Going to a 34-inch seat pitch (still better than most of the airlines) would probably see Regional Coach cars go from 72 seats at present to somewhere in the ballpark of 80-86 seats (depending on precisely what the situation is with luggage racks and ADA seating requirements). Ramming that pitch down to 32 inches could get you a bit more density...but at that point you might also be looking at needing multiple business class cars or going to a de facto three-class model (e.g. Coach, Premium Coach, and Business).
Finally, (4): I'd like to see Amtrak keep the student discount, but it really shouldn't be tied to an independent membership card. I also remember being told a few years ago that the Student Advantage discount transitioned to online-only at the same time as they dropped it from 15% to 10% (something of a mild annoyance) and was no longer usable in conjunction with upgraded fares (which rendered it useless for me). I'd say that Amtrak should, if anything, look to make the discount a bit more aggressive (perhaps effectively putting it in line with saver fares) but also aggressively promote it and not make it online-only.