DCC coupling of N-hydroxysuccinimide and 2,2-dimethoxyacetic acid I am forming N-hydroxysuccinimide ester (1) by DCC coupling with N-hydroxysuccinimide and 2,2-dimethoxyacetic acid using distilled THF as solvent.

What I see on $\ce{^1H}$-NMR is three major singlets:
$\delta~\pu{4.840 ppm}~(1\ce{H}),$ $\delta~\pu{3.432 ppm}~(7.26\ce{H}),$ $\delta ~\pu{2.731 ppm}~(6.36\ce{H})$ and some impurities.
While the chemical shifts are well-aligned with theoretical predictions (in my opinion), integration ratios do not quite make sense. I wish I could purify it to have a clearer NMR spectrum and see whether I actually have the desired product, but I don't think my ester will stay stable in silica in column chromatography. Any suggestions?
If peaks for "some impurities" are appear around $\delta \: \pu{1.8 ppm}$, I assume you have residual THF in your crude product. The other multiplet of THF is probably burried under $\delta \: \pu{3.43 ppm}$ resonance. That would confirmed by your impurity integration, which should be equal to 1H unit equivalence. If I'm right, your 6.36H unit equivalence is actually overlap one of $\ce{CH3}$-resonance and one of $\ce{CH2}$-resonance.

On the other hand, the two resonances at $\delta \: \pu{3.43 ppm}$ and $\delta \: \pu{2.73 ppm}$ would very well be representing two $\ce{CH3}$-groups and (two $\ce{CH2}$-groups + part of THF impurity), respectively, as well.