Not sure how the lacing system affects the arch of your foot, since the arch is on the sole of your foot. If you have a high arch, you might want to consider a footbed with arch support. I use Aetrex supports, personally, though there are many others you can try. I would talk to someone knowledgeable about fitting shoes (a good shoe store; someone at your LBS who is trained to fit shoes; or better yet a podiatrist).
Lacing would affect your instep. If you have a high instep, then you may need more room than is normally available in a standard cycling shoe. Some shoes have adjustable retention straps at the top. I've never tried any of the boa systems, I hear that the dual boa systems (separate boa laces for top and bottom of foot) are best in these circumstances, but I can't say from personal experience.
A high instep often goes along with difficulty with heel lift, I hear that there are shoes with mouldable heel cups, you might look into that.
If you have a wide foot, you might try Sidi Megas or any of the other shoes known to have wider toe boxes (Northwave, I hear, Lake possibly - sorry, I've never tried them). I did try Carnacs, but the footbed was a terrible fit for me, and this was before I had switched to my own footbed recommended by my podiatrist so I didn't try them with a better footbed.
I have wide (EEE) feet, with a high arch and a high instep. Like you, I've had trouble with straps too tight across my instep, heel lift, cramped toes and cramping feet. I've been using Sidi Mega Genius shoes, with the top padded strap moved out to a setting where it is centered on my foot when tightened, and an arch support footbed with a metatarsal button (you can see why it might be best to talk to a podiatrist) for the past 15+ years, and that works well for me. The shoe is comfortable enough for me to cycle up to 6 hours without discomfort, and the footbed helps to support my arches and to hold my heel in position. I do still sometimes get some numbness, and in hot weather I have to remember to loosen all my shoe straps after a while or I get a hotfoot under the ball of my foot, but overall this solution has worked well. I'd really like to try a boa shoe one of these days to see if it would be better, but I'm cautious about messing with something that isn't broken.
Last edited by noimagination; 09-25-18 at 06:22 AM.