Knowing N Wales pretty well, as I do although mostly the N.W. - it won't be the A55 as that has a pretty reasonably alright cycleway along next to it (in no small measure thanks to Roy Spillsbury of the CTC - thankyou Roy) - can take you at least three times as long cycling W, along it sometimes though!
There are often not really anything like direct alternatives to the main routes in that area. Of course be useful to have a better idea of where your route is. . .
One thing though, I find particularly in an area like that it is mostly the same traffic you meet each day - so after a little while they get used to expecting you as a feature of their journey. I find this helps a lot, especially if you acknowledge particularly the one's that slow down and give you loads of room. You are establishing yourself as a feature of their journey at a good time of year now.
At the moment I find myself often commuting a particularly crap section of the A470 in mid-Wales. I find the lorries, particularly the timber lorries (to and from Newbridge mill) are a) regularly up and down - so get to know you. and b) Amongst all the traffic most consistently and sometimes patiently overtake me in the text book way that they should, as do the local taxis and school buses. I think the trick of it is to inoffensively assert your right to be there while having a good regard for your safety.
I hope it pans out well for you, these things are often worse to think about than to actually do.