Matt, I know I'm late to the party, but I do have two cents I'd like to throw in.
I, like others have voiced, think they shouldn't be cut up simply because it would be a shame to undo what has somehow survived for 50+ years.
But, I understand the monetary aspect of it, so consider the following.
I've been collecting uncut Post panels for about a dozen years now. When I first started the rule of thumb was that the complete panel was worth about twice the sum of the value of the individual cards. I've always tried not to pay more than twice the individual card values for a panel and was often able to get some for less. In the last couple of years, it seems things have changed, especially for 1963 panels (which unfortunately you don't have). It's very rare for a panel to go for less than twice the sum of the individual card values. Even panels from 1962 (which are more common than panels from 1961 or 1963) can sell for more than twice the value of the individual cards. One thing that helps the value of the panel is having the ads still on the panels, which yours have.
You should also consider that keeping the panels intact also means you would avoid the grading fees. Plus keeping the panels intact also means that you don't have to worry about cutting the cards so that they can get a numerical grade (this is especially true for the 1961 panels).
Bottom line, I think if you were to cut the panels up, you would not be able to sell the individually graded cards that you are lucky to get out of them for more than you would get for the panels.
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