Looks like I'm gonna have to go with option 1 but could run pipes through studwork then exist out from side of wall rather than digging out floor and crossing over?
Only concern and it is a showstopper, is if that is artex and it's pre '92 then it could/probably will have asbestos in it. That's a major no no if you want to channel it.
If it isn't then just channel the wall and then run the pipework within than. Quite straightforward with an angle grinder and stone cutting blade and a nice sharp cold chisel, if it's brick .... it will be messy/dusty tho.