A tang sight can be used with almost any front sight, since it sits behind the receiver (unlike a side-mounted peep), and can be adjusted high/low enough to align with the issue line-of-sights.
The only problem is, that if the issue height is used (as you found out), the rear barrel sight intrudes on the peep sight picture - and needs to be either removed or folded down (Marble's makes both a short and a long-leaf folding rear barrel sight).
On rifles that I want to use the tang peep for all shooting distances, I simply remove the rear sight & fill the slot.
On other rifles, I zero the barrel sight for short yardage (snap/brush hunting shots), then fold it down to zero the tang sight for a longer distance.
Both rear sights are zeroed using the same front sight.
I find there's usually enough time to fold the barrel sight and raise the tang for a shot at game some distance away, but not the reverse for game close at hand.
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