Your remote plumbing plan sounds very similar to the one I am helping set up for what seems to be a very similar tank. The main concern I see is that while a 2" drain pipe will handle thousands of gallons per hour (even at 30' away), it does require some head-pressure to do so. Since you are going to be building a sump at a very low drop compared to the main tank, you would not be able to pump as much as say, if the sump were, 3' below. OR, FWIW, what is the flow if both tank's water levels are equal...well, nothing. On the system I am working on, we are using two 2" bulkheads, and two 3" drain pipes to flow to a sump system that is 10' away, and has a water level 12-18" below that of the display. We dont know what we will be able to get for out maximum flow yet, and we are prepared to lower the sumps another 6-18" if we need to (Tank will be 24-30" tall on a 36" stand with a 18-24" square base center overflow, no standpipes, but "squat" dursos to prevent air intake, pretty much a "U" on the bulkhead...just bottom 2" bulkheads, 500g, intake sump is a 180g/24"h on a 24" stand 10' away in the next room). We are going to start with one 3000gph high flow pump as the return on a 2" return line, and go from there...maybe adding a second pump later.
Heres what I would do. Build it how you want, but be prepared to drop the sump 6-18" if your overflow isnt keeping up with the return pump. I have done the math, but there are simply too many variables, esp considering the 30' length you have. There are a few things you can do to help. You can use one size larger pipe than your pump and overflow bulkhead need. Using 2" pipe on your drain will help greatly over two 1" lines. And your return line, if it is 1" at the pump, use 1.5" until it gets to the tank to minimize loss. And heres the funny thing...pumps this size wont have a huge head loss if they have to pump up only a foot or two. Sure, for pumps that only do 500-1000gph, a 3' head and multiple elbows can drop your throughput significantly, but with 1000+ gph pumps, even if low flow...look at their power curves. Many lower pressure ones still have no problem pushing water up 12'...and 1 or 2 feet wont add up to much loss. Your overflow does seem a little restrictive for what you want to do...the only way to know for sure is to set it up and find out...being prepared to drop the sump a bit more if needed. OR, you could lower the sump throughput. DNA's sump for his 300g is only 100gph...now that might be tha extreme case, but even if you were to drop your overflow capacity to 400-600gph, thats still more than 1x the volume per hour, up to 2x. I dont think your chiller would have that hard of a time keeping up...
"Should I plan a larger capacity drop in unit for my sump to simplify things with this new setup?"
As I was reading the few sentences before this, its exactly what I was thinking as well. A drop in would simplify things...otherwise, a closed loop off of the sump would be my second choice.
Wait, Anchorage, Alaska? And you are worried about heat? Wow, must be a medeterranian current up there. FWIW, my place is run with minimal air-conditioning...in fact the fish tanks get minimal cooling..at best they get a fan blowing across the surface here in Milwaukee, and we have had many hot days here this summer.
I wouldnt be worried...unless the change in temp from the lighting/pumps on the display is so huge the chiller will be working nonstop evn with the lights off. I doubt it will be a problem. Your display volume of over 300g would require many thousand watts of lighting in the course of its daily photoperiod of about 8 hours to raise temps much. Welcome to the world of large tanks...things sort of work themselves out at this size, LOL. Not to mention, 1000 gph of sump flow from the chiller should be plenty to cool a 300g any day. Its like my pond, 3000g. It can be 100 degrees outside all day long and the hottest it will get is 85...as long as the night comes and it has a chance to cool, its fine. Now, if the nights were as warm as the days, my Koi would be screwed...but that isnt the case. This relates to your tank as well.
If you are in an extreme situation, and you want to maximize your chiller's potential, there are some things you can do. One, mount the temp probe in the main tank and the chiller in the sump. If the chiller has a hard time catching up ever, it will simply cool the sump's water to be that much cooler to compensate. This is an advantage that an in-line temp probe on a in-line chiller wont have. A drop in, with a remote temp probe will. This of course means: You will need to keep this final cooling chamber in your sump seperate from your fuge, skimmer feed, etc...as you wouldnt want that extra cooled water flowing through your refugium or frag growout tank if its plumbed from this same chamber. It might also help to try and insulate this chamber so that your freshly cooled water doesnt just end up cooling your sump room. You will not have to add extra capacity to this area however, as we are dealing with the deltas in temperature here with regards to what will be a fixed throughput...a larger volume means nothing. The added benefit of this will be that if the water that is going through your sump return pump is cooler, you will not have nearly as much calcium buildup on the internals.