If you want to reduce your worm count longterm you may want to think along the following:
1) Close your herd (and your sheep flock as well if you keep them). At least for females.
2) House your goats over winter (at least 6 months) and worm them at the start of housing. Check worm counts post worming in case you have resistance. (if the goats have worms you will need to use a clinically proven wormer, garlic etc will not work). Your grazing should be clear after 6 months' rest, though if you are down south and the winter is mild that may not be 100% in which case you may have to not grfaze them for a whole year, but instead have a hard standing area for them to mooch about, and bring their greens to them - branches mainly in summer, plus really good hay.
3) If you keep sheep as well, make sure they do not share grazing with the goats and also try and reduce their worm burden by worming when necessary, preferably with a wormer to which there is absolutely no resistance. The main thing is not to bring in new animals, if you bring in males -worm and quarantaine until worm count is clear. Same for bringing in bily goats.
4) If you need to use an external billy - do not board your goats somewhere else, but sponge them if you need to travel a long way and/or billy owner has limited days available.
I haven't wormed my goats for a long time now, same for sheep. I do not graze the goats in rotation, sheep rotate between two fields and are never housed.
As to supplements - my ladies will not eat garlic! They do have a copper rich lick (Red Rockie) and are drenched with a sheep mineral drench containing copper once or twice per year. Some of them will eat seaweed as if it is the best thing ever, others will not touch it and won't eat any of their concentrates if seaweed is sprinkled on top. I have not seen any difference in performance between the seaweed eaters and the "not in my bowl" group.
For GG's a supplementary diet of oats and sugar beet shreds may be ok, if you feel that is less like a concentrate feed. When mine are dry they only get a tiny amount of these two, but when in milk I also feed a calf mix (and/or dairy cattle nuts) in addition to oats/shreds. I also like to feed Alfa A over winter instead of concentrate. GG's can get fat quite quickly on concentrates. Not sure there are organic options for sugar beet shreds or oats that won't need a second mortgage though...
Hope this helps.