I'm planning on going back for a bikefit and have said since I ordered it that I'd be interested in seeing if a stem change would help.
That's probably a good idea, and get them to look at the positioning of the levers then too, as you shouldn't struggle to brake from the drops. Even if it's not something you do often, you want to be able to do it comfortably and effectively when you need to.
Quite a bit of travel on the brake levers, I tightened the back one but couldn't really work out what I was doing with the front, so even more annoyingly I ended up with different pull on each lever!
If you do a google search it seems that lever travel is a noted feature/issue with the Hy/Rds. Apparently it's just how they work. Do your levers come back and touch the bars when you squeeze hard? If so it needs looking at, but otherwise it might just be something you need to get used to. I am looking to get new calipers for my CX bike and was put off the Hy/Rds for this reason as I don't like a long lever pull.
Incidentally, I picked my bike up from the LBS at the weekend and the mechanic commented how much he liked my brakes compared to his discs. I asked him if he had BB5s, expecting he must have something inferior, but it turned out he had Hy/Rds. Apparently he found the Spyres on mine far easier to adjust and less faffy. I thought it would be the other way around tbh.
Any time I was in the big front ring I was getting chain rub noise, so that needs a little tweak and there were times when the cassette was jumping a bit. I'm assuming this is due to the lbs not quite getting it set up right, rather than an issue with Tiagra so can't mark it as a bad point of the bike.
That's poor on the bike shop's part. I have only been riding a year and am still pretty rubbish at most mechanical things but even I can index the gears and set up the front derailleur properly. Check out the GCN videos on Youtube for how-tos - I had no clue but learned in half an hour and a bit of trial and error from them. The rear will likely just need a few turns of the barrel adjuster - turn in towards the bike if the gears and jumping down the cog/not changing up smoothly, away from the bike if they are jumping up/not changing down smoothly. It's a doddle if you have a work stand and can turn the cranks and change gears while tweaking the barrel adjuster - you'll be able to hear from the sound of the chain chattering against the sprockets when it's slightly out of whack and, then a nice smooth sound as you turn the barrel to tweak the cable to the right tension.
I think part of the problem with the front one is the disc doesn't look like it's central between the pads, which I think means I need to undo the bolts mounting it to the frame slightly to tweak it.
Do you mean the rotor is set at an angle? If so it will need adjusting, but if it's parallel with the pads but further away from one you will just need to turn the pad in on that side. Not had a close look at Hy/Rds but with my Spyres it's a simple slot on the caliper - you just insert the correct sized allen key and turn clockwise to move the pad in, anti to bring it out.