Some Conti road tires can be very difficult to fit on many rims. Ultra Sport II are tough as well. Same with a Vredestein Fortezza Tri Comp I mounted recently. Ditto Schwalbe One V-Guards from a couplafew years ago.
Get a Kool Stop bead jack. I rarely leave home without it stuffed in my jersey pocket, in case I flat on the road. I like Conti tires but it's almost impossible to horse 'em across some rims without leverage. And it's more difficult now with arthritis in my fingers and wrists, especially in chilly or wet weather.
There are more compact bead jacks but they don't offer the same leverage. The Kool Stop is a bit bulkier but about the same size and weight as my Topeak RaceRocket HP mini pump, so not a big deal. Sure beats wrestling with tire levers and causing pinch flats (yup, done it with brand new tubes), or making the Call of Shame.
Powdering the tube and bead can help. I used Monkey Butt skin powder the other day, since it's all I have (talc free too). Helped a lot.
Velox and other cloth tape hasn't been a problem as long as I get the narrowest tape that covers the spoke nipple holes. If the tape is wide enough to climb up the rim shoulders it'll probably hinder seating the bead. I think I use 10mm or 12mm at widest.
Not all Conti road tires are that tight. I recently tried the Grand Prix Classics, 700x25 skinwalls, and they fit fairly easily the first time, and more easily the second after the mold release and bead edge was burnished a bit from previous mounting.