Hi Art
You are having a frustrating time!
I think church records for Kilkerrin/Clonberne Parish begin late (I just checked) in or around 1892 (for baptisms), so I assume the Winifred Mullen Baptism was not relevant to your search. In lieu of actual records or concrete information all you can do is to continue to collect what info you can and see if, over time you can connect names like Mullen to the Gavin's etc etc through the various bits and pieces you find. If for example you were to find a marriage record for a Mullins that includes the names of witnesses that were Gavins you could be more certain that they were connected to your family.
In terms of collecting more info, your main task should be to collect everything you can about Mullen/Mullins in Kilkerrin:
(1) include the 2 John Mullins listed in the Tithe Applot. Books on the National Archives website in 1827 in the townlands of Shankill and Big Meadow, (google 'national archives' Ireland and 'Tithes' and the database will appear, it is similar to the Census database and easy to use)
Again they may not be relevant but until such time as you can rule them out it is better to include them as relevant until you can make an informed decision.
(2) You could have a look at the Clonberne Parish website and see if you could contact someone through that who would know the area better or indeed know someone who knows someone:
http://homepage.eircom.net/~clonberne/
(3) Exhaust your search on Roots Ireland for baptisms, marriages and deaths. If they are not there it is because the records don't exist, because the area is wrong or the surname is worng, though they usually search under variants of surnames to catch all the different spelling. Check the Tithes through the link above and check the Griffith's valuation and print it all out and re-asssess what you have.
You may find that the info you have is all you will find (I hope not), but given that your ancestors emigrated in the mid-1800s and most parish records haven't even started by then, you may be stuck. Surely they didn't all emigrate though, so there have to be some around after this and up to this day. At least you will have tried everything.
Also have a look at the Ordnance Survey Map for Ireland, you can access the Historical Archive and see the Parish down to the individual townlands with all the old wells, forts etc listed. It won't tell you anything you don't already know but it is nice to get a feel for the place. Check the County Coucnil website frim time to time to see if any of the graveyards are added to the Galway County Council website. The Council has an on-going project whereby some parishes are uploading graveyards memorials - http://www.galway.ie/en/Services/Heritage/Graveyards/
If all else fails and you come across something that you think might be relavent but isn't related to Kilkerrin remember the neighbouring Parishes in the area - Moylough, Kilbegnet, Boyounagh, Ballynakill. Have a look at the Irish Times Website, unfortunately it a subscription one, but she how you are fixed
http://www.irishtimes.com/ancestor/fuses/townlands/index.cfm?fuseaction=TownlandsInCivil&civilparishid=1036&civilparish=Kilkerrin&citycounty=Galway
Good Luck
Mrs Doyle