Let's see, here are some follow-up ideas, based on Ecorce's and poosticks7's:
*To adapt the number of FP to the size of the group, maybe we could say that every character has as many Fellowship tick boxes as the number of companions.
But, to be nearer to the RAW's ratio of recovery (although a bit under it, i think, which is positive for me), I'd allow 1 point recovered for each box ticked; that is, as every interaction between two characters means that each one will tick one box, that's 2 Fellowship points per interaction.
The group of 3 will be able to recover in the whole Adventure phase between 6 and 8 FP. I find it very interesting that, if only two of the characters do interactions between them, the total number of FP recovered is lower than if the interactions are spread among the whole group. Very thematic.
*Hobbits and Honey-cakes: Each Virtue/Blessing/Reward that would usually add 1 point to the Fellwship pool, now allows the character who has it to add one extra tick box to his character only. This allows for one more interaction in the group and, therefore, for 2 more points recovered.
*Rangers: Different options could be shuffled (for example, that they don't count as a companions when calculating the number of tick boxes), but I like this one at first sight: they count as a companion when calculating the number of tick boxes, and they themselves have tick boxes as everyone else, but their tick boxes don't add points to the Fellowship when filled. Each interaction with a Ranger only adds 1 point to the Fellowship pool, instead of the usual 2. Others may find confort and security, even esteem, on a Ranger. But they themselves know that they have a duty that's greater than their personal relationships.
On top of that, Rangers still can't take points from the Fellowship pool to recover their own Hope.
*And last, about the skill checks. I'm tending towards the idea that no roll is needed, just the roleplay. The tick boxes already offer a limitation, so that I don't feel another one is needed. And it would widen the possibilities of the scenes, allowing to not always rely on the same skills where the characters have good ratings. Maybe I'd say that an interaction scene can only be roleplayed after any common skill roll (even if it's a failure), so as to remark that something was at stake there. The scene has of course to be related to the outcome of the roll and the intent of the skill check. It might be very interesting to hear how the players come up with a good story about how their bonds tightened when one of them failed an Athletics test with an Eye while trying to hold the other one from falling off a cliff...

Let's see what you think.