Looking at where you are I wonder why you feel a need to move your breeding activities into a greenhouse. As cold as it gets here (-12 degrees F some years, usually -5), about the only use I would have for a greenhouse would be to keep very tender breeders and seedlings from freezing in the winter, and to keep fresh pollinations dry for a day during the hybridizing season.
Your winters don’t get cold enough for long enough that you need to worry about most of the classic HT’s surviving.
Your summer is plenty long enough to overfill the larder with hips without needing to extend it at either end.
I realize this is your first year and you want to speed things along with your greenhouse but choosing some new breeders and propagating them over this winter might be more efficient in the long run than indoor hybridizing.
If you were to decide to work with species roses your greenhouse would be invaluable to overwinter the first couple of generations of crosses against very tender partners because such progeny tend to be tender themselves. It would also allow you to stable some of the species that need winter protection like roxburghii, wichuraiana, chinensis spontanea and gigantea.
Mister Lincoln is very woody for an HT and it actually likes a bit of winter. Despite it’s disease problems it has promise as a breeder for winter hardiness because it otherwise offers a suitable package of refinements - remontancy, poly-petally, petal size and substance, bright white parenchyma in the petals, fragrance, pigment density and complexity - and good fertility and broad cross-compatibility. For that reason it is also a good choice for pairing in species crosses and, in fact, is one of the few breeders I have had success with using moyesii pollen and pollen of Eddies Jewel (but not reciprocally, alas).
I’m reluctant to promote breeding with HT’s but you could consider using Tiffany, too, especially of you can find it VID, for the same strengths and with better fragrance but with the same limitations of disease and architecture. HT’s that are closer to the Pernetianas would give you greater pigment density at the expense of hardiness and the need for chemical life support but, again, if these were partnered with species roses then the compromises would be acceptable because the potential would be greater (imho): Soeur Thérèse, Pinocchio, Fashion, Spartan, Zorina.
Foundation breeders that would broaden your genetic base would be things like Joycie; Apricot Twist; Condoleeza; Dragons Blood; Sympathie; Robin Hood; Carefree Delight; Immensee and its derivatives; any of Griff Buck’s hybrids (getting to be hard to find); any Geschwind especially the setigeras (harder to find); Vielchenblau; descendents of McGredy’s Maxi; descendents of Horvath’s setigera Doubloons like Goldilocks/Allgold/Rumba (send me one too)/Watercolor; any Max Graf descendent of which Kordes has many; and Yellow Pages because it combines two important, relatively diverse lineages.
The strategy with these would be, of course, to target the usual physical refinements while selecting for disease resistance, vigor and hardiness.
Breeders that could be even more rewarding include the Barden Atomics - Castle Bravo, Canniken, Dakota Redwing and Diablo Hawk (Paul, what about Dominic Sunset?); Rupert’s Lynnie and his fedtschenkoana derivitives; Rippetoe’s bracteata’s; Harris’ R15-01 and derivitives; Davis’ Carefree Copper; Zlesak’s Oso’s; Sproul’s G-34 and I-89-2; and anything by Kuska that’s named after one of his relatives or comes from his giveaway seeds. Most of these are non-commercial, your mileage may vary.