How to add more OR searches with CONTAINS Brings Query to Crawl?

I'd be curious to see if a LEFT JOIN to an equivalent CONTAINSTABLE would perform any better. Something like:

SELECT     a.CollectionID
FROM       collections    a
INNER JOIN determinations b ON a.CollectionID = b.CollectionID 
LEFT JOIN CONTAINSTABLE(a, *, '"*fa*"') ct1 on a.CollectionID = ct1.[Key]
LEFT JOIN CONTAINSTABLE(b, *, '"*fa*"') ct2 on b.CollectionID = ct2.[Key]
WHERE      a.CollrTeam_Text LIKE '%fa%'
           OR ct1.[Key] IS NOT NULL
           OR ct2.[Key] IS NOT NULL

I was going to suggest to UNION each as their own query, but as I read your question I saw that you have found that. I can't think of a better way, so if it helps use it. The UNION method is a common approach to a poor performing query that has several OR conditions where each performs well on its own.