Botsari, by poor mending I did mean during downstream presentations (including dry fly skating). I'm not mending to increase fly depth, but to control what my fly is doing out there. My streams/rivers often have multiple fish holding structures (boulders, slots, sunken logs, and under overhanging branches and log jams) through the arc of one swing that can be fished more effectively by making my fly act as real as possible.
I want to be able to make my wet fly look like an actual emerging caddis or mayfly, and dry fly skating to look like an egg laying caddis, or one that is having trouble getting free from its shuck. I already do this with my single handers on smaller water, I want to be able to do it on bigger water as well. I want to cover as much water as possible with more realism than just a dead swing. Most of our trout here are intelligent, selective, and highly pressured. Realistic presentations catch fish.
"Classic" up or across stream (dead drift) dry fly mending I feel would only be effective with any rod at relatively close range when fishing across multiple current seams, or around obstructions which is the case on most of the waters I fish.
As far as my ideal line. I want it to cast as easy as a scandi, as far from my casting position as possible, with little to no shooting, with the ability to maximize realistic presentation by mending, all from an 11'3" 3wt spey rod (that still makes catching smaller fish fun). In short I want it all. I'm aware that this probably doesn't exist. But I'm willing to try different things to see how close I can get.
If you mean “little or no shooting of line” then there is zero problem as any head you can cast can easily be mended however you want with only a few feet of shooting line out the tip of the rod. Downstream presentations, even with more shooting line out, even fewer issues. Leaving aside what mending techniques you use which are pretty irrelevant, categorizing something like the Rio
single hand spey line as having inferior mending qualities doesn’t make any sense at all in this context. It’s just not computing, sorry. So trying to figure out what you are actually saying is not easy.
It appears all you are asking is if there is a longer head you can spey cast on a 3 wt switch rod.
If you want an off the shelf line that is relatively easy to cast that has a head around 34’, not including a tapered leader then try the Rio
SH Spey line already suggested. If you want even longer try one of those, but there are, as you have already figured out, not a ton out there at that wt - I think none specifically optimized for “ease of spey casting” at that weight longer than that line. I think the ballistic vectors are the longest off the shelf SPEY lines at the very low weight end of the spectrum and perhaps, just barely, you could try the 4/5 at 41’ on that rod but it would probably be too heavy, and choking up a bit just turns it back into something closer to the SH Spey line.
Or save your time and just get Steve Godshall to build you one from specs you think you want - so much easier doing it that way at the extreme light weight end of things. It will cost the same and be less frustrating looking for, or otherwises cobbling together a line. Steve is the MAN for this - he has regular customers that fish 80’ heads on crazy custom 5 wt spey rods so your spec interests here are quite moderate compared to that. As an added benefit when you contact him he will be able to provide a one-stop reality check on whether something you want to try can work. He has told me a few times when he thought what I asked for was not physically workable as a line - I have a bad habit of asking for “the same thing but 10’ longer this time”.
Presentation CONTROL is IMO an issue somewhat orthogonal to the line length, but if you are talking about quarted downstream then seriously consider the well establish and highly effective solution to this problem - a longer rod. They are an acquired taste at that wt, but are a possible answer to pushing the boundaries, and will make life so much more pleasant is the spec range you seem to be interested in.