Most tarantula venoms are extremely weak... even weaker than garden spiders in many cases. If you would get something like a rose hair (Grammastola Rosea) or a pink toe (avicularia avicularia) the chances of you getting bitten are VERY VERY low... in fact I don't know of a pink toe ever biting someone before. That particular species just never seems to want to bite. Rose hairs are very mellow and fairly slow spiders that are well known for their docility.
A lot of tarantula bites that I hear and read about are dry bites too.
Basically with the more placid species of spider (like pink toes, rose hairs, PZB's or chacos) if you dont muck with them your chances of being bitten are pretty much zero. I presume you won't be trying to handle them anyway so that decreases the slim to none chance of a bite even more.
If you would like, I extend this offer to you or dragon... I will give you a rose hair tarantula free of charge (pay the shipping and she is all yours) It will be worth it to me to see 2 more cases of arachnophobia cured