Grounding electrical sub panel in separate structure
You have a 5th option if no grounding path is available and you want to update. Current code allows for a separate grounding conductor to be added to be compliant with 4 wire feed (if not metal conduit approved for use as such).
And a 6th option, install a GFCI breaker or receptacle at the first device in each branch circuit. This is the same option that allows 2 wire receptacles in homes to be converted to 3 wire and a tag stating no equipment ground on the receptacle (they come with these stickers pre printed).
Your system is the same as any home built prior to 1999 is it really hazardous? Code allowed this for almost 100 years.
If it was really hazardous code would have changed much earlier in my opinion.
Having a separate grounding conductor makes sense even if you have a grounding electrode at the detached building. Most non electricians spout all kinds hazards but think about this the grounding conductor can be smaller and if a large current is on that conductor there will be a larger voltage drop so is it really that much safer? , how many electrocutions do you hear about? Not many to start with.
Your #1 would be just like a new install but now that you updated the panel most jurisdictions want all the receptacles to now meet code every circuit with a receptacle requires GFCI protection (yes even lighting there are no exceptions unless local).
Your #2 put a GFCI on the feed at the house panel. I hope you are trying to get in shape because not only is this expensive you will be making a lot of trips to the house to reset it (GFCI’s do not use ground, but they do use the neutral code defines them differently grounding / grounded).
Your #3 install a transformer 1:1  again an expensive task it creates a separately derived system and you can now bond the neutral and ground in the main Panel it is no longer a sub 15kva 1:1  $600+ new $400-500 with shipping eBay used (shipping hurts here).
Your #4 leave it as it is, understanding millions of homes have this same setup.
As you can tell I might suggest running a new grounding conductor at the most. Possibly GFCI breakers or receptacles but I don’t have them in my shop. I have a customer that calls me almost every other month to replace a GFCI receptacle on one of his 3 saws he is afraid of electricity even though he has never been shocked and had me add GFCI receptacles almost 10 years ago well before they were required.