WALL OF TEXT follows. Sorry. Hopefully it's a wall of text that helps you or someone else.
Don't panic! It's likely fixable without too much redesign or additional supplies.
1. Sag!
Sag isn't really a problem as long as the hut clears your tent and everything stays connected. But there are some common sources with easy checks.
1.A. Do the two spine pieces fit loosely in the X connector or does it take a teeny bit of effort to pull them out? If loose, take some duct tape and wrap it around the ends of the spines. You're trying to get juuuuust enough wraps that you can still get them connected if you push, but all the extra space is filled up.
1.B. If you look at the picture, the middle arch of the ribs is flatter at the top than the outer arches. Is the sleeve connecting these two ribs longer than the other sleeves? They all need to be the same length - and centered - for the rib arches to all have the same shape. Longer sleeve = flatter top = lower center height on that one rib.
1.C. Sag like you have can also happen quite easily once there is already a (non-symmetric) curve bent into your PVC. Try taking each of the center rib pieces out one at a time and turning them around so the end that's near the ground is now at the spine.
1.D. To keep everything connected, I use a rope or some ratchet straps. After the PVC is up but before I put the tarps on, I either take a long piece of rope (not paracord if you can help it, something less stretchy) and run it next to the spine on one side, tying clove hitches around each rib to snug it close into the connectors OR I do the same thing with ratchet straps. With ratchet straps usually they will do a 5" length of spine so I run a loop around each two neighbor ribs, alternating what side of the spine I'm on. When you do this, it will also tend to straighten out your spine as long as you don't over-tighten.
All of this should fix your sag enough.
2. Dimensions!
2.A. I have a nerdy spreadsheet I made that calculates the ellipticals. If you bring the width of the monkey hut in to 11', your center height is 7'2". At 10.5' it's 7'4". And at 10', your center height is 7'7". I believe, based on looking at that tent you linked, that at a width of 10' you should just clear the corners of the tent. At an elevation of 5'10", the ribs of the 10' wide hut each come in by ~1'9" leaving a width of 6'6". If you set up your tent poles and measure across the top pole & connectors, is it less than this? If so, it'll fit - you don't need feet of clearance in every single edge of the tent, just healthy air gaps at top and sides.
2.B. If the tent's top is wider than this, or for some reason you want more room in the hut, the general diameter expansion method you proposed (lengthening the ribs) will work fine to get you extra height & width, and is the most efficient way to do it. However, don't do it by putting (2) 2' extensions on the edge of the ribs! Either put (1) extension in the center (you can shorten the center sleeve if you go this route since there won't be a join under it) OR make your extensions at least 3' longer than the top of your rebar and also shorten the ribs you have now to get the total rib length you want. The reason is that you don't want a sleeved joint too close to your rebar or you have a tendency to break the sleeve at the join.
2.B.i. If you extend the diameter of the hut (length of the ribs) then as Jovankat said, one dimension of your tarp is just the total length of one rib arch. For example, 2 pieces of 10' PVC => 20' on one edge of your tarp. 2 pieces of 4' + 2 pieces of 8' => 24' tarp edge. The other dimension of your tarp is governed by length below.
2.B.ii. However, nobody says your tarp has to go all the way to the ground. It's a little more dusty, and you need to have faith in your guy lines since there will be more uplift on the hut -- but if you don't have the money to buy another huge tarp then the one you've got is just fine!
2.C. For length - yeah, you'll possibly want a longer hut since your tent is 8' deep and the sun comes in from the side a lot.
No worries there - just extend length exactly as you showed in your drawing, with more connectors, more spine, and more ribs. Personally I like to have a length that's at least twice my tent depth and then I put the tent about 2/3 of the way down it so I have a shady "front porch" to sit in.
2.C.i. The second dimension of your tarp is the total length of all your spine sections (aka the length of the monkey hut). 2 pieces of 5' PVC => 10' long. 4 pieces of 5' PVC => 20' long.
2.C.ii. BUT you will have a very convenient rib right where your current tarp ends. And you can still use your current tarp and just buy a new tarp for the part you added on.
So in summary, if it were me (making some assumptions about what you want to spend to fix this)
- check sag
- measure top of tent: less than 6'6" wide?
- if yes, re-pitch monkey hut at 10' wide and try tent under it now
- if no, make 4' extensions for current ribs and cut existing down to 8' [alternately, if you have the cash, I'd go with (4) 6' sections so it's all the same part]
- decide on desired length: I recommend 20'
- if you do 20' I personally would just buy one more 10' x ~20'-24' tarp; install both (use the shorter tarp for the section over your tent, if one is shorter); and live with the gap.
Gotta beer? 