I'm in the middle of a similar project in the PNW. Removal of invasives on about 2 acres followed by native replantings. The method and timing of all this took a bit of research with some assistance from state/county resources.

This is my basic approach:

1. Identify which invasives were "highest" priority for removal immediately and come up with a plan for when and how to remove them. I have a lot of invasives so I'm actually phasing this work out over several years and tackling my lowest priority invasives in later years. Garlic Mustard would probably be higher priority than the Herb Robert in your case. You would need to research what herbicide is most effective with Garlic Mustard and what time of year it should be applied. You might also need to research how to time herbicide application around rain or pollinator seasons (or even time of day if doing foliar spraying). Check if your county has a noxious weed specialist you can email - I found mine very helpful and they were able to confirm my plan made sense and point me to resources. The more I researched eradication of different invasives the more I realized how incorrect most of the advice is on herbicide use and control methods. And not every landscaping company would be an expert in every invasive either, especially if it's quite new in the area.

2. Get a list together of native plants that work well together and check if your county has a "Conservation District" plant sale. In my area they only let you pick them up once a year, which happens to be the time of year that they can be most successfully replanted (around the rainy season).

3. Monitor regrowth in following years and manually pull or spot treat.

Thanks for restoring your woodland!