Any advice for longer (3 months) home exchanges?

For a three month stay, make sure it is less than 90 days.

And the 90 days includes both the day you arrive in Denmark and the day you fly home.

Although, come to think of it, Denmark has a special, extra-Schengen deal for US citizens. Maybe the time limit there is more than 90 days if you haven't spent time in another Schengen country first?? I'm not sure.

Although, come to think of it, Denmark has a special, extra-Schengen
deal for US citizens. Maybe the time limit there is more than 90 days
if you haven't spent time in another Schengen country first?? I'm not
sure.

That deal is that US citizens may spend 90 days in Denmark, irrespective of time spent in other non-Nordic Schengen countries.

Thanks, Badger, so it's still 90 days altogether. I didn't remember whether the extra time in Denmark was 90 days or 180 days.

Correct, but it also means that a side trip to Germany for a few days will give you a few days extra in Denmark. That can be enough to be able to stay three months.

We’ve done 20+ home exchanges in Europe for 3-5 weeks and rented our home four times for 4 months. The big differences for us for the one month vs multi month arrangement (and exchange vs rental) is about utility bill paying. For a direct exchange of 3-5 weeks we always each paid our own utility bills. When we were renting to a visiting faculty member for a semester, they paid our utility bills. I would think with a direct, longer exchange you could both pay your own utility bills if the number of people were almost equal. Also if your exchange family has extremely high costs for something like electricity be respectful of any restrictions they ask you to do.

Otherwise we never had any pitfalls, we just tried to keep good communication going before the exchange. We list a reliable family member or neighbor as a contact person. Also we try to ask and answer questions thoroughly before the exchange and let them enjoy themselves during the exchange and try not to bother them during the exchange.

We have used the agency and one other to find our European exchanges without any problems.

I put together a binder with lots of information, so everything was in one place. This included appliance owners’ manuals. On three different exchanges, we were faced with mysterious appliance operations. I guess people must think that the way things operate in their country will be obvious. In a Danish apartment, for example, the clothes dryer became less efficient with each use. We bumped into someone from the building and seized the opportunity to ask about it. Turns out that there was no venting to the outside. Moisture was collected in a compartment which had to be emptied manually. Who knew?
Another time, in France, we couldn’t get the ac working, and it was quite hot. The English abilities of the exchangers was so poor, as to be indecipherable. There were several other issues; and the adult son, who lived nearby, was unresponsive.
I would specifically ask exchangers to leave operating instructions, preferably those that came with the
appliances.
*Despite some irritations, we have enjoyed all the exchanges.

I am sorry, rosalyn.
The phrase " the adult son, who lived nearby, was unresponsive " could be the title of a one act play, that many of us could write.

I once managed to lock myself outdoors on a second floor screen porch and eventually alerted neighbors to free me. The home owners (friends who were away for the weekend) put a hidden key under an end table going forward