Not a fortune and could be useful elsewhere.
I don't have TV, so won't be much use I don't think:
If it's an FM aerial, it won't be much use for TV, but might be able to boost a sensitive portable radio or whatever.
I thought the aerial was an omni; in which case I doubt that twiddling with its orientation would yield much if anything. If you want to try, instead of trying to 'hear' improvements whilst on the job, why not simply turn the antenna by a few degrees (as surely you must have it pointing roughly in the right direction already), studying results for a day, then repeating in the opposite direction.
Personally, I think you're snookered, as even throwing money at getting a good FM stereo signal on the off-chance of reasonable success, I really don't think your tuners warrant it or maybe possibly within the capabilities of your ancillary kit. Don't think internet radio, of which I have no knowledge/experience, would be the best way forward, if feasible in your location/situation.
As mentioned, I have experience of trying (and failing) to get FM stereo in Pembrokeshire, but in Saundersfoot on the flat south coast. Though if you're nearer the Preseli Hills north of Haverfordwest, albeit 9 (crow's miles?) away from the TX, it could be tricky indeed. Matter of interest, do you have decent portable radios in the house and if so, what's reception like on their antennae? It would be a guide if nothing else.