Work on resetting pavers on the patio after a heavy rain

I wouldn't go forward with that plan.

Diverting the water three feet away from the foundation won't stop the water from getting to your foundation. You need to put a french drain in and ensure that there is an outlet for the water to go somewhere where it won't damange anything.

You can buy premade french drain material at your local home improvement store of you can building your own with gravel and perforated pipe. It's generally pretty cheap either way.

Also, ensure that you have proper slope for your french drain or you won't have flow like you need to ensure that the water gets moving.

Best is probably a combination of french drain and pulling it all up and regrading the base. Also the most hassle and expense, but in terms of function, the best option. And you would then have the option of running the drain under the patio, if that helped with discharging it.

The individual pieces of that that you have thought of are somewhere else along the expense and hassle line, as well as the effectiveness line. Obviously pulling up a few pavers and repacking under them is least expensive, but it will help the water to move away - but if the patio as a whole is not sloped to drain well, it won't help much if you are just moving the puddles around. So, if just a few spots are low, it might be all that's needed, but if filling one low spot will simply result in another, regrading the whole thing looks better eventually.