It's not F-22 vs SAM. It's system vs system. There's ECM, cruise missiles, special forces, buying the manual from a disgruntled/greedy Almaz employee etc. There's another issue. The price of the missile and how many are procured vs how many decoys the US has.
The fact that such a SAM platform is in need of destroying implies its the early stages of the war, possibly even the first hours, against an advanced enemy and all assets are available.
Depending on who is initiating the war, the US might have had RQ-170's flying in the area for days prior to the conflict, gathering elint and learning every frequency hop and pulse combination said radar uses.
F-15's deploy a swarm of MALD-J's over the area while GEO-2 satellites overhead are watching for radar and IR emissions. The radar site in question engages some of the MALDs, immediately giving away the GPS coordinates of it's TEL's to the satellites. F-22's hidden amongst the MALDs engage the TEL's from range using SDB's.
F-22's already have a reasonable idea of the location of the radar using RWR triangulation, and the spy satellites are already hard at work performing detailed scans of the box where the F-22's detected the emissions source. The satellites use radar, passive IR (looking for potential hot power generators, or even a hot array) and other passive means to locate and generate a coordinate for the radar.
Ship or B-2 launched tomahawks, or F-22 launched SDB's are used to finish the job, the latter being the cheapest.
I find it interesting that while there are some improvements being made to HARM there isn't a replacement program.
It seems that SAMs will be dispatched with other munitions. This is because they can shut down and nullify the ARM seeker. Instead of putting a secondary seeker on an ARM, why not put an ARM seeker on another system or just use a different type of guidance that doesn't rely upon the SAM emitting?
You can always throw walls of projectiles back at a CIWS. Land-based CIWS would be protecting either less mobile and more fragile assets. It makes a lot of sense for a ship, but is impractical for land use. Don't dismiss the fact that computer-aimed AAA can already target rockets and bombs, it is just no a CIWS.
Guys, the OPs post asked about LPI SAM radars. Most of the stuff you suggested relied on you knowing where the radar was. If it's truly a LPI radar you wont even know you've been painted until the SAM pops up and it'll never come up on the RWR so you won't get any sort of line to the transmitter.
Also, could a MALD really duplicate/generate the returns an LPI radar is expecting? In all those frequencies and at the right pulse interval? Surely if it just buzzes in blasting out signals in all frequencies it would be recognized as a decoy.