Approaches to creating recurrent seedlings from species

Not likely due to the timelines and space requirements, but I still fantasize about bringing a couple species roses into very modern lines of roses.
If I (on paper) want to marry traits of 2 species and obtain something recurrent, is it better to cross the species with one another first, and then do 2 more crosses with a selected seedlings of successive generations to get to remontancy, or cross both with rebloomers in the first generations and take a long-shot crap-shoot trying to get an F2 seedling that is remontant?

My impulse is towards the latter, but have seen multiple threads (as well as well-documented hybrids) in which hybridizers are doing the former – crossing the two non-remontant species right off the bat.

What would benefits be of both approaches?

From my reading of the forum’s threads, I’d say it depends on which species, because chromosome-number. Most species are 2n-diploid, but many are not (and even the “nots” vary in number and breeding behaviours). The most common repeat-flowering roses available are the 4n-tetraploid Hybrid Teas, Floribundas, Austins, etc., though diploid (and triploid!) lines exist too.

Most who’ve gone the route you’re talking recommend making the species x species crosses first, then going for repeat with those hybrids, or even F2 seedlings from sibling-crosses from the species-hybrid plants.