OK, I finished my challenge run this morning. These were the restrictions: no purchasable Nosferatu (I didn't preclude the possibility of the one freebie tome, but I never wound up using it), no Sol skill (again, I didn't preclude the possibility of the dropped sword, but in practice I needed neither the skill nor the sword), no Veteran, no Renown/Wi-Fi anything, no skirmishes, no event tile items or weapons, no Rally Spectrum. Also, full deployment was required in every level in an attempt to prevent tiny teams from trivializing the game (though I can't say this worked all too well; a Second Seal ban would have done more to prevent this), and also to make stages like Ch 21 more interesting. There may have been more restrictions, but those are the ones I remember. Avatar was not allowed to engage in combat if she was Paired during Prologue through Ch 2, inclusive; as soon as Ch 3 began, I removed Veteran and allowed her to fight while Paired. My restrictions did not preclude children Paralogues, but I wound up not having to go to any of them. Chrom finished the campaign at 20 Lord/11? Great Lord, which ought to establish that there was no real Aether abuse.
The game still felt really imbalanced, though, largely because of Panne, whose Wind/bow weakness can be played around really easily due to her high HP, high Def, and respectable Res, along with Physic staves and her high Avoid (aided by an S support from Lon'qu as well as Quick Burn, Tantivy, and Even Rhythm). There is a good case for her being even stronger than non-Nosferatu, Veteran-using Avatar in a leisurely playthrough, as she trades bow/Wind weaknesses in exchange for being much more durable against everything else; Avatar won't have the Avoid-stacking options that Panne does if Avatar remains in magic-using classes.
The main reason I didn't ban Panne at the start was that I didn't want the run to be too challenging; I wanted it to be hard enough to be engaging, but not so hard as to make me pull out my hair (unfortunately, it was not much more challenging than a typical run, which just goes to show how unbalanced Lunatic is). From what Interceptor has shown, however, I feel like banning Panne could be worked around pretty easily by investing in Nowi. Banning Second Seals entirely can prevent both Panne and Nowi from trivializing the game, but there are probably other tricks that you could use, such as pumping all statboosters on a single unit to approach stat caps, or by getting children with good skillsets (such as Severa with Rally Def from Kellam and Rally Spd from Cordelia). rsteube on GameFAQs claims to have done the game without Second Seals and with "only one Master Seal [on each character]," and I believe him; things like Rally Spectrum and Naga's Tear, neither of which he seems to have banned in his run from what I've read, can really trivialize the game in addition to having good Rallybots like the aforementioned Severa.