I suppose the information we are missing is how long it takes the gate to establish the node and if capable how long it takes to collapse the node using it.
If both are short, an hour or two then for example then precautionary shut down would probably be the best bet unless you believe GTVA survivors could slip though.
If the shut down is longer than transit time or not possible but the gate wont take long to reestablish the link then move up the meson and be ready, perhaps shut down the gate structure and move it to keep it safe.
This is of course academic for a while if the UEF warships are limited to intra system because then you would be looking at days or months of refit if possible before a counter strike could be mounted.
Before any blockade can reasonably happen, all GTVA forces in Sol must also be destroyed or forced to withdraw.
Seeing as that's pretty much impossible to do without losing the majority of the rest of the combined UEF fleets, that's not a likely outcome. The losses would mostly rack up because in order to force all GTVA forces out of Sol, you'd have to attack all of them and defeat them simultaneously, or the damaged ships will simply be replaced in a few days.
if the UEF capture or destroy the remaining logistics ships then they could feasibly weaken the GTVA logistics capability enough to force withdrawl out of system as remember they are not just big freighters but also repair workshops.
The UEF warships will probably be at or beyond 3000 meters from the node to minimize return fire, in which case what is the point of sending a Meson ship to blast the blockade if all you are reasonably get is a few fighter/bombers?
Clearing the fighters is the first step to clearing the node. Whether the comparative expenses are justified misses the point that if you have only one way back in you're going to use it, and this is the first step.
The GTVA probably already has this capability, it'd be of use against the Shivans in multiple roles. (It's not just good at breaking up blockades, but would make effective way to cover a retreat through a node or just ruin the day of ship concentrations.) The bombs could easily just be sitting there, ready to go, for any old target.
Even just demonstrating the capability might be worth it. The UEF can't be sure how willing the GTVA will be to pull the trigger. It would put a serious damper on any plans to operate near the node even temporarily, like interdicting supply runs.
Personally I find that a bit thin, while the demonstration of a Meson warhead would rattle the UEF ships the fact that it reinforces the Do-or-Die situation means they woul dhave no choice but to fortify the node and make absolutely sure such devices do not make it into the system