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The best stuff for boat engine compartments will, sadly, be marine grade. There are a couple of products that look like foam rubber with a layer of lead or dense vinyl and a mylar face (over the foam) to keep oil out of it. Sold in rolls or tiles to be cut and glued up, or self-stick, like what you're scraping off.
The problem with the stuff in the auto/home stores is that the foam may not stand up to the moisture and heat in an engine compartment--and it should be flame resistant, too. Then there's quality...even JCWhitney used to sell this stuff but their quality has been known to vary.
The lead/vinyl absorbs energy just because it is so dense. The foam decouples that vibration from the engine compartment walls, and in theory you get less noise. There are usually special mounts/ties that will also let you hang the stuff so that they take some of the weight (from the dense layer) and still decouple some of the noise. This is one of those jobs where there's enough labor that it is worth doing the job "right" with better materials the first time.
There are also some sound absorbing coatings that are sold, kinda like a gallon of heavy silicon rubber, that are supposed to work well--but they're designed more to keep thin metal/frp panels from vibrating and resonating, the thick foam+lead stuff still is unmatched.
"Acoustic controls" and "soundproofing" suppliers on the web usually turn this stuff up, but the good stuff is never cheap.