Hill climbs require you to have good standing stamina and as high lactic acid tolerance as you can.
I agree with the second half, but I would be riding the hill at threshold level sitting down. Yesterday`s ride, I went from the onsen we were staying at to the top of the road I was on, which was 550m in 10.5K and it was all sitting. Today, I rode back home (75K) and included about 950m of climbing, again all seated, even with my backpack. If I`m riding at my limit, that limit will be higher/further if sitting when climbing rather than standing. I would only stand for temporary relief from sitting, or powering over a very short, sharp gradient section.
For hill climbing , climbing at your lactate threshold is a good way to improve. By climbing at threshold your body adapts to raise the threshold so you can do more work aerobically. A good workout is two climbs of 20 minute duration at lactate threshold (for me 170 HR).
I agree with this, limitation of your ability is your sustainable threshold level for the duration of the climb. So working out how long the climb will take you and doing a full TT effort for this length of time, would for me be a better strategy than very short hill repeats, especially as you have the long climbing at the weekend. Or add say +10% to the time, divide by 2 and do 2 sets of that. So say 1 x 45 or 2 x 25. You can then use the perceived effort scale when doing the actual hill climb to adjust your gear and/or cadence to match this sustainable power output for the duration of the climb. Obviously if you are lucky enough to have a power meter (not me) this makes it a lot easier to do.