There are many replacement piano style hinges available, it may be best to take your old one along and match as best you can. You may consider replacing it with a more stout hinge and may have to purchase one & cut it to length.
To "drill out" the spot welds, take a used drill bit approximately the same diameter or perhaps a size larger than the diameter of the spot welds you wish to remove. Reshape the end of the drill bit on a grinder to remove almost all of the existing bit angle, keep a container of cool water handy to keep the drill bit cool while grinding the angle to almost flat. You want the leading edge to still cut metal, but at an almost flat profile.
Center punch each spot weld & drill a "starter" hole using a two size smaller regular drill bit almost half way through the hinge side only. Then using the flat ground bit with the pilot hole as a center, drill slowly from the hinge side ( which is to be discarded) until you have almost punctured the hinge, take care NOT to drill through to any of the lid portion behind the hinge you wish to save. A little practice on the technique & tweaking (sharpening) the drill bit angle on a piece of scrap sheet metal and you will see how easy it is. The existing screws I noticed in your photos will need their holes filled by either welding (tig) or JB weld.
The paint looks very damaged in places, if you decide to try & save it, you may consider air brushing with many light coats to fill in the bad spots & blending with block & color sanding then buffing. Getting the correct shade of touch up paint will be the issue, but an experienced automotive paint shop would be the best place to get advice on how to achieve the correct shade. It certainly will never be as good as media blast (soda), etch primer, & repaint, especially once the hinge is removed, but I admire your desire to try & keep it as original as possible.
Contact your local welding company if they do not do spot welding (using a machine)
I am sure they can offer who in your area does this type of work.
