hau Eric, all I can say about your bounty of
wood chips is "what a problem to have!"
Asparagus that comes from big box stores is almost always Martha Washington variety (at least that's the only one I've found at any of ours here in Arkansas).
How many years has this bed been set? MW can produce well for up to around 20 years, and it will survive neglect.
Case in point, in Alberta, Canada I am aware of a field (probably around 100 acres) that has been producing MW spears for over 50 years now, the owners passed to the spirit world about 35 years ago and the family, while still owning the farm, does nothing with this
land.
The people that live in the nearby town go out and harvest spears for 8 weeks every year, the field is full of "weeds" since it has not been tended to for 35 years.
So, while I wouldn't worry much about the bed's current condition, laying on wood chips would only hinder the current crowns production in my opinion.
Straw would be a kinder to the new spears (fiddle heads of the asparagus fern) but if you want to introduce a new species of crowns, then either would be grand for the soil.
Using wood chips, I would give them a soak in mushroom slurry prior to laying them over the current bed and I would later on give a spray of compost tea, just to get things really rolling along.
Mycellium do not increase heat nor do they raise salts content of soils, it is bacteria that cause the heating of a compost heap and wood chip heaps work the same way.
Of
course you could do this and then simply make the bed either larger overall or longer by adding your new species crowns or end up with an interspersed bed since most likely not all the current crowns would die out.
Redhawk