With the utmost deference to the AHS inspectors, if they thought that nice mare of yours was a F1 they need get more exposure to full grown TBs!
Your mare is lovely, but that’s what TBs look like once they’re fully mature and in an exceptional program as yours no doubt is. Your mare is a GC granddaughter (very common in race bred TBs these days) and he stamped consistently. Here is GC for reference:
His favorite son of mine (for sport) is a carbon copy:
Your mare has a common pedigree (common in the sense many of these stallions are in dirt and turf racing pedigrees - not common as in derisive). GC earned huge commercial success, as did Indian Charlie (Uncle Mo) and even Regal Classic – who was quite heavily used in NY and I saw many of his offspring at sales and end-of-meet listings. They made great eventers. From a racing standpoint, this is a pretty common assortment of well-known sires to feature on a page. Aragorn himself is as US-bred as they come despite the IRE tag - so don’t let anyone who isn’t experienced with TBs tell you your mare’s conformation is unusual among race horses.
Your mare has plenty of bone (for a TB) in her pedigree and it should be coming through, but one thing about your mare’s sire line is they can grow rather slow – but are very precocious from an early age.
With most modern WB stallions today you might find your mare’s bone matches theirs and you may have to breed back to a more heavy stud to get that ideal you’re looking for. TBs in the last 15-20 years have gotten quite big in frame and bone, in part thanks to a fair bit of linebreeding to common stallions that were not toothpick legged in any shape of the word. My Say Florida Sandy TB has thicker bone/substance than my Sir James filly – and she hasn’t had a TB in 6 generations.
You mentioned no hunter-type stallions, but Hanoverian has no shortage that can jump and cross well with TBs. Rubinero, Rubignon and Quaterback come to mind as stallions that add bone to TB mares and cross quite well.
Since you mentioned bone specifically, Jaguar Mail will add bone even to TB mares, but I don’t remember if he is approved Hanoverian.
It really depends on the end goal for this offspring. Upper level? You may want to consider a proven UL producer, like Windfall or Tatendrang (neither Hanoverian) - both pair exceptionally with TB mares. An all arounder who might clock Prelim at best? Consider stallions who have broad exposure to a lot of mares and seem to make good citizens - like Navarone, Belissmo M, Redwine, or Gatsby.