I have been a new car Service and Parts manager for thirty years. I'm not going to tell you this won't work but there are a few things to think about here. In order for it to work the first thing that is going to happen is that you are going to have to thin out the oil, if your engine is as sludged up as you say it is more than likely the oil passages are clogged as well. If by some miracle this flushing system works, that means that all that sludge and crud will be washing through your engine, thru your main bearings, thru your cam bearings, thru your oil filter and thru your pickup screen. There are only a few places sledge can collect, the top of the heads, the lifter valley and the oil pan are the most likely. If your main concern is on top of tour heads, take off the valve covers, take off the rockers, get a putty knife and clean out the crap as best you can. Years ago when we had an engine with a clogged lifter or sledge buildup we use to put Marvel Mystery Oil in with the oil to unclog the lifter or to help loosen the sledge. Run the motor for a bit then change the oil and filter. I use to sell BG products at the dealership, about $40,000 a years worth, but to be honest it was basically just a profit maker. Ya they had all kinds of documentation showing how well it worked, but to be honest it was a gaff just to make money. It is my belief that most of these miracle services that are going to clean your engine, or stop oil leaks, or make your tranny like new do not work, they are just another way to make money. Naturally the things I am saying are my opinion, but my opinions are based on 35 plus years of working in service departments and building engines. Another thing to think of is if they are going to pump a solution thru your engine under pressure you run the risk of blowing out your rear main seal and other engine seals. If your problem is as severe as you think, I believe the only way to fix it is to take it apart and clean it by hand, to have all that crap washing thru your engine at 3000 rpm is not the ideal solution. Best of luck to you in whatever you decide, I hope everything works out ok for you. Here is a website for you to check out if you want.
http://www.nordicgroup.us/oil.htm
Here is a quote from this site regarding oil flushes;
Engine Flushes--The Latest Scam
Engine flushes pump heated solvent through your engine, supposedly to wash away sludge. But regular oil changes with detergent oil already take care of the sludge problem. And if you actually have an engine that is full of sludge the last thing you want to do is do an engine flush because the sludge can clog the oil passages and destroy the engine completely. These flushes are completely unnecessary. All they do is wash the money out of your wallet. As Click and Clack state: "This is what's known in the business as a "profit center." Something the garage can use to beef up the amount each person spends per visit. So unless you've got a very old car, and are trying to solve a specific, sludge- or carbon-related-problem, I'd skip the R-2000." These engine flushes usually sell for about $130. The victims are people that think that they are doing something nice for their vehicle by cleaning the engine. In fact a dealer or repair shop that tries to sell you an engine flush should be avoided for all service because they are untrustworthy.