Hmmmm....Brown to red does sound more like a clayey soil with good clay content...that is strange?? How hot are you get this oven and for how long?? They are o.k. with cooking temps, but prolong temps higher than that shortens there serviceable life span unless lined with soapstone or firebrick...
...would adding too much sand make it weak/crumbly if it was actually clay and not silt?
"Grog" and/or silicates (aka sand) can augment and strengthen a clay for firing, yet there is also a thing about too much...testing tells a lot, but one brick is not "testing."
Firing questions: is there any obvious way to tell what silt/clay content is?
Other than learning some basic geology, and soil science with the correct equipment (e.g. microscope, soil screens, etc.) the best way is to send samples away, and also do more "fire testing" of tiles...and...brick samples.
You can try the "patching" and do let us know how it goes...but my experience tells me it is a wasted effort and your best time is spent "testing" and deconstruction while at the same time planning for a better built oven...
Regards,
j