If Bessey K style are not in the budget, Bessey H pipe end clamps are very economical, with new lengths available for the price of an iron (or steel) pipe.
Found these on Amazon UK
Use waterproof glue, make the joint tight-fitting, and leave the screws on the shelf. A lap joint is one of the strongest of all the glued wood joints, and a well-fitted glued lap joint will be at least as strong without the screws as with them.
But... there's a condition. How wide are the two planks forming that joint? And which wood is being used? I ask because of wood's inherent expansion/contraction with humidity/moisture changes. If the joint is too wide for that species of wood, and the wood isn't extremely well sealed against moisture intrusion, then expansion/contraction will destroy the joint; nearly all woods expand & contract across the grain far more than they do along the grain. As the wood becomes moist, it'll become wider but not longer.
Certain woods have a very low expansion/contraction rate. Other woods have a very high expansion/contraction rate.
If the wood is extremely well sealed, its inherent expansion/contraction will be minimized, but can never be totally eliminated (there's no such thing as a perfect seal).
If you're using wide boards, and that species of wood is subject to high expansion/contraction, then neither glue nor screws will prevent the joint from failing. Better in such a case to make a different type of joint, like a dovetailed saddle joint pinned across the "inside" corner, for example. That's much more difficult to make, though. Another option would be a long mortise with a tenon narrower than the length of the mortise.
Good outdoor gate joints are difficult things to make, since they're exposed to the weather and tend to collect pockets of water after a rain.
Best Answer
Slightly contrarian take: start over.
(I know, you've done a bunch of work, etc. They call it the sunk-cost fallacy for a reason. Strong butt joints in the rail are possible but hard and would involve a ton of wood filler afterwards.)
Get another door. Rough cut next to the hinge stile (but not cutting off the molding on the stile). Extract the panels and cut them to size -- no difficult joining. Clean off the dregs of the rails beside the stile. Cut your rails to an appropriate width and use whatever joinery seems best. (You'll probably need to do a bit of chisel work to flatten out the molding where the butt of the rail meets the stile.) I'd biscuit for alignment, then after glue-up is dry, sink 8-10" structural screws (2 or 3 per rail). 1/2" dowels would be good as well, as long as you were drilling the holes for them when the door was glued up and flat. Trying to drill two sides of the dowel separately is a recipe for frustration and alignment disaster.
--- Edit ---
Here's a series of pics that show what I'm talking about above.
Starting point. Sorry about the rotation.
Rough cut the rail. Don't cut any of the molding on the stile.
Mark where the rail copes over the molding on the stile. You'll cut that part of the stile later.
The molding on the stile runs all the way through under the coped rail. Somehow, chip/cut away the remaining rail.
You can do part of it with a chopsaw (granted, awkward with an 82" stile and impossible for the midrail), but don't cut past your pencil line. You'll inevitably be left with some wood that the chopsaw won't touch, so chisel/ multitool/ whatever to clean that flat.
Cut the miter that you marked with the pencil earlier on the stile molding. (Don't do what I did and bust off some of the molding while demolishing the remainder of the rail.)
Cut the rail to width and miter the molding.
Your parts should go together perfectly. Join them as described above.