With Oliver having the Stanlake name as a middle name I would tend to work towards connections between the Stanlake and Balkwill names. Oliver also seems to be a name used by the Stanlake's.

An Oliver Stendlake was baptised at Black Torrington in 1833 son of a Richard & Grace Stendlake who also baptised other children in the Parish. I can't see any Balkwill's being baptised in this parish around the 1834 period.

As Holsworthy, Cookbury & Black Torrington are adjacent parishes or very close it's possible these families are connected.

There was a strong Methodist movement in the area. Non-conformist registers have not always survived or been deposited with Registry Offices so possible this is why you can't find a baptism for him.

I would be tempted to do a lot more research on the Richard Balkwill who married Mary Stenlake as always dubious about information I find on various sites. Have you tried contacting the person who have Richard & Mary emigrating and asking what records they hold to substantiate this fact.

It's possible that Richard moved from the area, married someone else after Mary died, have you checked for her death before 1841. Status is sometimes recorded incorrectly on marriage entries or if prior to 1837 not given.

RG4 & RG8 which are held at National Archives, Devon RO's have copies, are I believe on Findmypast. They are under Non-Conformist Record set on Findmypast and it might be worth browsing these for the Holsworthy area. Also check on Devon Heritage Centre online Catalogue to see what Non-Conformist records they hold for the area you need.

Also look at alternative parish records for the Holsworthy, Black Torrington, Cookbury area. I've solved some problems similar to this by seeing things such as removal, settlement, bastardy orders, parish poor relief payments, apprenticeship records etc.

Just a few quick thoughts.