Hi 348/340HP
Just happen to have one of those 348's myself in a 61 Impala Convertible.
I would recommend you go with the 62 "used" radio. In the first place, it is the authentic one and secondly, it is a better radio. As you pointed out, it is all transistor while the 61 is a Hybrid (both tubes and transistors).
By "stiff pushbuttons" I assume you mean 'mechanically'. That is an easy owner fix. Remove the covers from the radio to expose the PB mechanisam and lubricate with light machine oil such as 3-in-1. While in there use the air hose to blow all the dust and debris out. Be careful not to get any lubricant on the rubber clutch disc. Clean the PB's with "Pledge" or simular product.
The 'screen' over the speaker is to keep the dust and bugs out as the speaker faces 'up' and once something falls inside it is a real nuisance. It can just as well be covered with the fine mesh plastic screen-wire (paint it black). You may also purchase simular material at a fabric store.
The speaker for this unit is unique, but in most cases can be 're-coned'. You may contact me direct for a source or ship it to me.
Good luck on your project.

:rolleyes: