Although not "conventional" in terms of front versus back nines...but how about the routing at Lawsonia links which starts at hole #9 and goes 5-3-5-3-5-3...you gotta love it!!!
What's interesting about Langford's famous non-par-4 stretch at Lawsonia is that it melds with his thinking about golf in general, and in particular approach shots into green. Langford was a fairly prolific writer, and in one article for a golf publication he suggests he's more interested in varying the lengths and types of approach shots into greens than he is with conventional notions of par.
At Lawsonia, the stretch of non-par-4s begins on #9 with a 535-yard par 5 (short iron approach), a 239-yd par 3 (a fairway wood for most), a 498-yd par 5 (fairway wood for the better player, wedge/short iron for the rest), a 183-yd par 3 (mid-to-long iron), a 568-yd par 5 (with a severely uphill 3rd shot, even if it's a short iron), and a 154-yd par 3 (that is slightly downhill, perhaps a club less, and a short iron for most). (Lengths are from the tips of a 6,764-yard course, designed in 1930.)
Interestingly, this stretch is immediately preceded by another interesting array of holes that call for approach shots of: short-iron/wedge (#8, 339 par 4), mid-short iron (#7, the boxcar hole, 161 par 3), long iron (#6, 431 par 4, possibly shorter iron due to downhill LZ for fairway), fairway wood (#5, 487 par 5, with possible low-to-even-mid-iron 2nd shot if you really catch the downhill LZ), long-iron/fairway wood (#4, uphill, Redan-esque 203 par 3).
Combined, the 10-hole stretch provides tremendous variety in the clubs players will use to hit into greens -- for me, a real hallmark of a great course, and very much a deliberate part of Langford's routing and design scheme.