Sue,
Just some comments:
>The veneer does not always have to be removed. If it is already mostly loose and coming off then you can carefully remove the rest of it and then clean each piece and reglue it.
>If the edges of the top have gotten wet and come unglued, then you can use a plastic credit card, or a hacksaw blade to work the glue under the pieces and then thoroughly clamp them overnight.
>Delaminated plywood is also fixable. It takes time and a lot of clamping but can be done to look good.
Having said that, yours is going to need much work. You will need to find pieces of the same kind of wood and carefully graft them into the missing places after you've glued the original pieces down. Finding wood of the same kind can be very difficult. Even modern veneer of the same wood may not match the original grain pattern. But it can be done.
When making patches use a straight edge to follow the grain and cut it at a 45º angle in the big part. Cut the patch edges at a 45º angle also then glue and clamp them together. Buy using angle cuts the edges glue down stronger and tend to disappear as you sand them.
If you choose to completely remove the veneer and replace it, you'll need to thoroughly clean and sand the base wood. The local wood shop I get my veneer from said they use a contact cement to put their veneer on the base wood. I used a wood glue and had problems when I did the top of my 9W-7 treadle. Had I to do this one over again I'd reuse the original pieces of veneer.
It will need to be sanded smooth and stained to match as well. It is a time consuming project but it can be done.
I have a three part thread here where I told about redoing a treadle that was once used as an aquarium stand. The machine was undamaged, but the wood was seriously damaged. Here's the three threads.
{
http://www.quiltingboard.com/vintage...e-t194998.html
}
{
http://www.quiltingboard.com/vintage...e-t204377.html }
{
http://www.quiltingboard.com/vintage...n-t218398.html }
Good luck, have patience, take your time and it will look good again.
Joe