Here's a thought... Lectra Motive Cleaner
. Can also be found at auto parts stores, Walmart, and on occasion RV parts stores.
The following is a long story to tell you this can of cleaner may get you going if it's only in need of cleaning, and you can get access with a spray straw to have a solution before it warms up.
Sometimes when getting access to the electrical parts due to confined spaces, you can get away with spraying it down with the above from the few access points.
Good example of use, the old I4 in GM vehicles in the 80's nicknamed the iron duke had a habit of developing an oil leak at the valve cover (among many other places) just above the starter and gumming it up. It was a weak point in the gasket and an easy inexpensive fix. Plenty of people would replace a starter every three months before figuring out the oil leak was causing premature failure. (why some mechanics were happy to do it without addressing the oil leak cause is another matter) I had a friend in college who's parents came to visit in an Olds 88 with this exact issue, they were having starter issues, and could not get the car started to get home. He called me for assistance, and after seeing it, determined it was from the oil leak, and they would be happy to pay me to replace the starter. Imagine their surprise when a (then) $5 can of electric parts cleaner fixed the issue enough for them to get home. My buddy and his dad then spent the next vacation at home replacing the valve cover gasket for a quality bonding moment. I even had the opportunity to participate via speaker phone.
Hope it helps.