Never managed to get into the park, but as far as I know you can't cross the borders whilst inside.
We went Ouaga - Fada N'Gourma (Belle Etoile is a great auberge, Ouaga side of Fada on the left as you enter just after the service station (which is on the right). From Fada we crossed into Benin at Nadiagouo (BF) - Porga (Benin) which had the greatest immigration police I've ever met in W.Africa, really friendly.
Tanguieta was where we were intending to get up to the park but didn't. Again, fantastic auberge, Le Baobab on the left as you enter Tanguieta ...
Sorry can't help with actual park details but both auberges will be able to assist!