Additional notes:
There are actually two construction zones. The more easterly, just east of the intersection with Lloyd Creek Rd, includes a temporary bridge, so no detour is required. (The early stages of the temporary bridge are visible in Google Earth imagery from 6 Jan 2018.) The more westerly, about half a mile east of the intersection in Lloyd, is the one requiring the detour.
I personally observed the latter construction on 10 June 2018. It was definitely impassable, a maze of rebar -- it's clear that this is a complete replacement of the bridge. I would not attempt it in hiking boots, much less in bicycling shoes. The natural conditions on both sides of the road make going around the construction on foot infeasible.
The web site (linked in the OP) says projected completion Spring 2019. North Florida has had far more rain than normal this summer, and I would not be surprised if this causes a slippage in the completion date.
The previously suggested detour via Springfield Rd is good. I rode the Gamble Rd and Springfield Rd parts of this detour on the same day that I observed the bridge construction. GSV imagery shows Springfield Rd as a dirt road in 2013, but the 6 Jan 2018 aerial view verifies that it is now paved, as does as my own experience in June 2018. However, I suggest that the best detour is to combine Springfield Rd with Whitehouse Rd between Capitola and Gamble Road. This only reduces the detour by a little over a mile, but it's prettier and has a bit less traffic. In fact, personally, I'd prefer this route as the main route.
EB: in Capitola, turn right on Whitehouse Rd. After about 4.6 miles, reach Gamble Rd / SR59 (stop sign and tee) and turn left. After 0.2 mile, turn right on Springfield Rd. After about 1.5 miles, reach Lloyd Creek Rd (stop sign and tee) and turn left. After about 1.7 miles, turn right on Old Lloyd Rd, using the temporary bridge and rejoining the route.
WB: after crossing the temporary bridge, turn left on Lloyd Creek Rd (the official detour), go about 1.7 miles and turn right on Springfield Rd. After about 1.5 miles, reach Gamble Rd / SR59 (stop sign and tee) and turn left. After 0.2 mile, turn right on Whitehouse Rd. After about 4.6 miles, reach Capitola Rd in Capitola; turn left to rejoin the route.
Edward