A couple things you may want to try that could help with increased walking on your trip...
1. hiking boots. Good running shoes allow you to roll over your foot which takes pressure off the healing plantar fascia better than unsupportive shoes. Hiking boots have a stiff sole that doesn't allow the foot to flex as much which is valuable for hiking (when on uneven ground / under the weight of a heavy backpack etc.). They are valuable when it comes to healing plantar fascia (even when not hiking) because they may allow you to walk longer when necessary without putting much increased stress on the foot. Although all tissue needs some stress to heal well (which is why your podiatrist is trying to get you to increase your walking a bit), the tissue needs to be supported well when increased activity is necessary (like your trip to Poland). Continue to wear your orthotics in your hiking boots as well.
2. Hiking poles allow you to take a little pressure off the lower extremities. The alternative is a cane....I just said hiking poles because I am used to dealing with a clientele that shudders at using a cane but feel they still look athletic / outdoorsy with hiking poles instead. If you opt for a cane, talk to you podiatrist or local physiotherapist to ensure you are walking with it correctly.

Unfortunately needs for life don't always jive with rehab needs. So these are just two ways that may allow you to do what you need to do while decreasing stress to those healing feet.

As for the other foot...it's hard to say from here but it is not uncommon to end up with some issues on the other side due to compensatory reasons. Basically, the body is not stupid! If something hurts, it tries to find ways to move that feels a little better. Unfortunately those compensations can lead to other issues. If you are actively dealing with the one foot, the other one will inadvertently be addressed so you don't have to fear that you are "falling apart"!

On a side note....what's your PhD....why are you walking in a forest in Poland? Sounds interesting!