Yes, Leeds probably is the closest parallel. The distinction I'd draw between us and them, though, is that they generally bought players who made the team better, while we made ours worse while similarly crippling ourselves financially.
I know that not all their signings came off, which is inevitable - Seth Johnson springs to mind. But we spent GBP 3.5 million, a huge sum, on our three most costly acquisitions - Daley, Reeves and Robinson. We got five years' service combined from the three of them and recouped GBP 800K in total upon selling them. Leeds paid a record fee for Rio Ferdinand but received even more when they sold him on.
IIRC, their undoing was that they gambled on making themselves annual CL qualifiers. The rewards for doing so then would have been vast in relative terms, but missing out twice, as they then did, left them in real trouble.
I suppose the big difference between them and us after relegation was that they faced an environment in which the financial chasm between the PL and CL was widening. When we went down twice in the 1980s, gate money was by a mile a club's principal source of revenue and the home club by then kept it all.
That allowed us to avoid catastrophic drops in income after being relegated. Unfortunately, having to pay GBP 500K per annum on our debts, a vast proportion of turnover, left us unable to compete with even clubs that could generate much less revenue than we could.