Hi,
When I look at the Nexperia 74HCT112 data sheet I would guess that it will be fast enough. You may have to buy a few and hand select. But, and it's a big but, they look to only be available in surface mount. No DIP part. :-( Going for a 74S112 from a NOS vendor would be the best solution I reckon. And. just in case a reminder is needed. eBay and various Chinese vendors sometimes end up delivering re-marked parts (whether this is deliberate or inadvertent is a discussion for another day), so testing/validating the part on the bench is essential IMHO. You don't want to be installing a re-marked LS part that will fade out as the temperature goes up, if it even managed it at the start.
Cheers, Brian.
Brian Cockburn