Babyjane - sorry haven't tried the product you're asking about, but I have used other probiotics over the years & wonder whether any of these might help if you haven't tried them already. If you need to get things moving, then Optibac Bifido & Fibre is said to be helpful, though personally it's not that useful for me.
Nature's Best do one called Acidophilus Extra (in 2 strengths) which also has the BB12 strain supposed to be beneficial for slow transit. I do find this effective in that respect but always had to take it for about 10 days before the effect kicked in properly. A word of caution though - I could never handle the 10 billion strength, but these days don't even tolerate the lower 4 billion strength well - seems to make my immune system go into overdrive making me feel feverish, so reluctantly I've shelved it. I also had the same problem with the probiotic VSL#3 which a NHS gastroenterologist prescribed for me. This is a multi-strain, high-potency preparation that is supposed to be very helpful & has good reviews. GPs can prescribe it, but it's not cheap.
I now take Optibac for Every Day which really helps me with feelings of inflammation & possibly also the IBS-C - I have gastritis & this probiotic seems to keep that under better control than prescription meds. The gastritis returns within a few days if I stop the probiotic.
There is a single strain probiotic from Quest called L Plantarum (Bodykind supply this mail order or online) that is supposed to be good for IBS-C & also for inflammation. I have had some success with this in both respects & it used to be the only one I could tolerate without unacceptable side effects, so I took it daily for a few years. I think it's very much a case of what suits one person doesn't suit another - which is why I've listed quite a few!
I also eat a high fibre diet, very little wheat & lots of live, natural yoghurt & keep fluid intake up, but as you'll know, in hypothyroidism, in spite of hormone levels within the ref range, IBS-C can still be a continual battle & again what suits one sufferer diet-wise will be all wrong for another. I can't tolerate flax seed, magnesium or coconut oil these days, as all seem to rev the thyroid.
A very good friend, a Microbiology PhD who worked on the development of probiotics, introduced me to them more than 30 years ago, so I find the subject fascinating! That said, whatever I take, I research it first, reading any scientific papers I can find, then reviews.
I'm still always very vigilant as I feel it's sensible to be extra cautious with auto immune conditions like Hashimoto's as probiotics are thought to have an effect on the immune system & patients with one auto immune condition are thought more likely to develop others. I think the field is very promising but that there's probably a lot more strain-specific research needed & that there may also be potential for harm.
I hope you manage to find something to help - the problem is a misery. Would be very interested to know if you do.
Wx