Just a few observations:
About 20-30 percent of the time I book a leisure rental, I will book it in my wife's name and then book a second under my name. It's a hassle (sort of), but my wife likes to drive and I hate to drive...but wifey only likes to drive in good weather. If it is going to be snowy, wet or windy, I cancel her reservation at the last minute and retain my reservation. Good weather, I cancel my reservation....works for us. But I always cancel the "second reservation."
In terms of last-minute price drops, they seem to be few and far between lately for me in the regions I travel. Rental car firms have been a bit dinged in the past several years and accordingly in general have shrunk their inventory as well as reduced staffing, at least according to the reports I have read in the business press. Which can mean fewer last-minute bargains.
Make no mistake, if there are cars on the lot and you make a last-minute pitch, there is a great chance of picking up a deal. But, in my experience the last couple of years, I am seeing more and more sell-outs of the particular vehicles I am willing to rent.
In the OPs case, there is nothing stopping her from going ahead and trying to make an online reservation right this minute under whatever name she wants, without touching the standing reservation that is in her name. If the reservation made right now is more expensive, I'd be tempted to go ahead and book it anyway (unless adding husband as second driver would be cheaper) as you never know what quote you will get later today, in the morning, or 49 hours from now.
Then, bargain with CS on the phone at your leisure.
The thing about car rentals, you can always cancel and it only takes a few moments to make an online reservation and only takes a few moments to cancel one.
In the case of ALLESONWONDERLAND, if rates have seriously doubled, it would most likely be much cheaper to just add a second driver to the existing contract (usually $10 extra per day). The second driver is always a nice option in my opinion....although seldom worth enough for me to want to pay extra for it.