that was my original plan. and certainly more elegant.... it is a long belly crawl though...and dirty.about 50 feet each way using my elbows to drag my ... .. the angles are pretty tough and the space is tight to make the joints . i would be soldering in my face..laying in positions that make my shoulders and neck cramp up. Ever get solder stuck to your eyelid? Yes I did... another story...and a lesson on safety glasses..
Two things got me to re-think my plans.. First. I checked my torch... the smell really bothered me and the space was not confined.. Add the solder and flux with no ventillation OMG! Secondly, the inside of the 'tee' fitting.. really rough inside with concentric rings from the manufacturing process.. Me thinks these 'tees' can introduce some down stream problems with the added turbulence.. At least that's what I read.... All that de-burring and then introduce these fittings?? Of course you have to use what is available...
So less crawling, less exposure to the torch.. less time..potentially fewer down stream problems. .Drill the holes. measure and mark the flex pipe, crawl, push the flex pipe in on one side, ties it up... maybe some plastic p-tape, push the other end up through the hole.,, then crawl out.. connection made under the sink with a shutoff and behind the fridge as needed... The span of the room is about 10 ft. add another 3-4 feet vertical to the valve a couple more to the box in the wall...