We're talking about trying to keep up with Nemona and I'm not even sure we'll get our first badge this FE, let alone our 2nd badge at the second FE.
Let's assume we find a new pokemon, and it's 1st-badge level to start (optimistic, but doable). To get our first badge, we've got to pass a DC 18 SKL roll. We have a 80% chance of passing that, which is good, but also a 20% chance of not (since pokemon badge levels don't seem to count for minor fights). Then, we've got to win a 2v3 against a Gym Leader. We'll have to start with our new pokemon, and win a 1v1. Then, hopefully wear down the second one enough for 2nd badge Roland to win a 1v2 with the leader escalating on their 3rd pick because they think we have a 3rd mon to use, which is dicey (I'd say ~50% chance).
Now, say we have our first badge. We're not going to get our 2nd without Renne fighting for us, so that's 4 AP for 4 weeks to try and get them ready to fight. But they need 8 bond points before they'll fight for us, which is 4-8 actions (last event we could get 1-2 bond points based on rolls). Maybe we'll get some bond points this FE, but probably not more than 2. So even will full investment we're not likely to have Renne willing to fight for us by the 2nd FE, and that is absolutely required, because fighting against a numbers advantage with equal badge levels and no type advantage is near impossible (assuming we also get our new PKM to 2nd badge)
We also only have 11 AP total until the 2nd FE, and 4 AP of that is going on Renne. That only leaves 7 AP for other actions - both training our new mon up to 2nd badge level, training Roland, and anything else we want to do. Evolving Roland takes 7-12 training actions depending on rolls, so it's not happening before 2nd FE (and also the mechanical gains for evolution are unclear, narratively it's a obvious power spike but in the mechanics?). And even if we got a 1st badge pokemon, and they gained some XP from the Gym Battle, it's probably still at least 3 Advanced Battle actions to get them to 2nd badge plus training their moves up which has more immediate boosts.
All this to say, because we chose Renne and her eventual power spike over immediate boost, we're not going to get a 2nd badge the 2nd FE. We might not even get our first badge this FE. Meanwhile Nemona will probably have 3 badges by then, and if not, she'll get her third during the 2nd FE.