It's fine to challenge players, but there's a point where the line can be crossed. Calling it 'real D&D' doesn't change that.
A few thoughts.
Short rests should be allowed after most combat encounters. That is one of the core assumptions of the design. A chase is fine, but that's an exception, not the rule.
It's not actually fun to force players to rely on at-wills for fear that they can't rely on the system as written working as it's expected to. They should be able to use their encouter and yes- daily powers.
I am also not sure why you can't just reduce the monster lineups in line with the party composition. 4e is pretty well balanced, across classes and monster roles as well as by party. Put in a bit less in the HP and AC department, and you won't miss that striker. Sure, add a new player if you want, but that should be based on suitability, not assumed combat role.
Also if you're requiring them to take on social skills, you should probably allow them a rebuild.
Skills are a weak point of the system; they are consistantly inconsistant in their usage depending on the game, group, classes, modules, ect. That's not on these players, or lfr. It's on the system, and everyone using it.
Requiring them to use a certain set of skills is an expectation that you're clearly adding after they built their pcs- you should have emphasised the issue before they built their pcs, but since you didn't, they should have the option of a full rebuild. After all, if they're going to be competitive with those skills in this new, toiugh game they're in, they may need a secondary stat at last in cha, and a few skills to capitalise on it.
You also have to be very clear with them what your expectations for the skills are- what exactly they can be used for, wether, as some gms use them, they're more of less interchangable, or wether, as some gms use them, they play the role very much as laid out in the book.
A good example of this: if a barbarian PC is warning an npc noble of a goblin horde soon to attack his lands, can they use their intimidate roll to, in good faith and without provocation, emphasise the threat the realm is under? Some gms will say 'sure thing', others will say 'no way!', it's up to you to make your views clear to the players.