Not every piggy clicks with every piggy, and that also includes boar-baby bondings. The advantage of boar dating at the rescue is that your boys can find "Mr Right" there from hopefully several candidates.
There are also several ways rescues bond.
"Full" or residential boar bonding means that a boar stays generally at the rescue for about a week, during which time he is introduced to up to three boars, but always with a cool-down respite in between and some time to meet the next boar through the bars first.
Whenever things go well, the bonding is then let to proceed over a couple of days and it is usually also stress tested to make sure that it survives the trip to new surroundings. By far not all rescues can offer this very time consuming service that also requires a lot of experience, but it allows the boars to get most of the crucial bit of the dominance phase out of the way before they come home. A resulting bond is generally as stable as a sow-sow bond. Fall-outs upon homecoming are rare.
"Speed-dating" at a the rescue (the dating variety Rainbow Rescue refers to) means that any boar is introduced to potentially several boars to find one he clicks with in the course of an afternoon, but this kind of dating looks only at initial acceptance and not at working through the dominance phase. The majority of rescues that offer boar dating only offer this kind due to their resources in terms of time - all rescues are volunteer run, and most of them do their volunteering next to a full job.
It means that you get the first hurdle (instant liking) out of the way, but not the second (dominance), and that there is always a certain smaller risk of things going wrong during the dominance phase. Boars, especially hormonal teenagers, generally go humping mad when meeting new friends of either gender, but you get exactly the same with intros at home, too. Bonding success usually depends on how humping much the more submissive piggy is willing to accept. A bond fails when one of the pair is fed up with being humped and is fighting back, the two boys cannot agree on taking turns or the humping from one of the boars becomes so excessive and incessant that it amounts to bullying.
By speed dating at the rescue, you can generally weed out the pairings where you have got two boars that are too dominant for each other and that clearly don't have a chance to last the distance.
However, going this way means that any failed boar can go back to the rescue and you usually get the support of the rescue especially during the first crucial couple of weeks.
Bonding at home means that you have to take both hurdles, acceptance AND dominance, all on your own and the risk of things not working out is accordingly higher. It doesn't mean that it cannot work, but it depends on you having a plan B or even a plan C at the ready in case bondings fail at any stage during the first two weeks.
It takes on average about 1-3 tries to find "Mr Right" during full boar dating at the rescue (for about 80-90% of boars), and about 95% of boars can find a mate within meeting 6 boars (i.e. two full boar dating stays, which can happen esepcially with teenage boars at the most difficult age for bonding); those percentages are the same whether you go rescue or do it all at home.
The crucial bit is - what do you do with the boars that don't work out, either at first sniff or those that are near misses?
Milhaven rescue in Keighley and BARC in Barnsley both offer full boar dating at minimal risk and effort for you, apart from the trip. Considering your anxiety issues, I personally feel that it would be the best option for you, as any bonding is going to be nerve-racking, even the ones that go well. That is an aspect you should seriously take into consideration under the circumstances. Your two boys are no longer easy-to-bond babies, they are full-blown teenagers.