…and I know one or two of you do, try Crippled Black Phoenix. This is The Heart of Every Country, from their Mankind, The Crafty Ape album, and this is a Journey cover, Of A Lifetime, off I, Vigilante. Killer guitar solo, too. These are the most overtly Pink Floyd tracks in there, but there is so much epic proggy goodness. They even give Echoes Part 1 a go.
I like all Pink Floyd so will have a listen regardless, but can you define what you mean by mid-period, do you mean Meddle, Obscured by Clouds etc? Or are you including post DSotM?
Good question. When I read the OP, I thought of the DSOTM through Animals period, but that could also be described as late period if you include The Wall. FWIW, DSOTM through The Wall are my favorites. I can rank them for you if you like. 
In any event, I’ll now go listen to the links.
I thought late period was the Wall through the post-Waters albums. I guess there’s really 4 periods:
Syd (1st two albums)
Experimental (up to and including Meddle)
Classic (DS thru Animals)
Late (Wall on)
Anyway, yeah, the vocalist is definitely a strong echo of Gilmour. 1st cut doesn’t really go anywhere-some reviews I found online decry them a bit for being too safe and “tame”…