Both are VERY possible, and may in fact offer some advantages to the original bed which, frankly, is a little small.
Most of the aftermarket bodies on beds offered usually include a bed at least 6' in length: the model A bed is more like 5'.
Width wise you're sort of limited to the distance between the fenders - although this can be improved upon slightly by using fenders originally from the closed body cars such as the Tudor and the 4 door. This techique was used in the production of the Station Wagons IIRC.
As to format of the bed, it is possible to take some lessons from the Model T era. I'll attach a pix which shows something typical of this era.
This bed is actually from Snyder's and is aimed at the 1926-27 Model T - but the dimensions are similar to the Model A and the adaptation should be straightforward. A little spendy at $800 - but one can reverse-engineer a lot of this.
Anyway, this a project near and dear to my heart as it will allow me to recycle a lot of the Model A parts that I own. And with a reproduction bed at $1600 plus delivery, it would for frugal me be a part of the truck which would NEVER be used - which kind of undoes the advantage of owning a truck?
But a wooden bed you could bang up with the rationale - if I need to I'll make another.
Funny thing the human mind...
Bring us pix of your project. We all LOOOOVE pix of course.
And welcome aboard!
Good luck,
Joe K