Calculating most abundant transcript from RNA-Seq data
Transcript abundance quantification is a tricky topic since a read often could belong to several transcripts, so any &quot;count&quot; is a best guess as to which transcript it actually originates from. That being said, there are tools that can help you here:

salmon (as you mentioned) to quanitfy. Run it with --numGibbsSamples 50 (or higher if your computer has the hardware. Also run with -d for the next tool
terminus is a tool that also originates from the COMBINE-lab, It's relatively experimental, but it applies well to your use case. It will take the salmon output and assign counts to transcript groups. If a set of transcripts can be clearly quantified above a certain confidence, that transcript will stay unique. If it is confounded with other transcripts, those will be placed in a transcript group and their counts will be summarised. More info here

You are right in that TPM, FPKM etc. are not appropriate measures to compare across samples. TMM, or DESeq2's median ratio method (what you get with counts(dds, normalized=TRUE) are a step in the right direction, but are still inappropriate across samples. I'd suggest this often posted blog post in the topic.
There are no perfect solutions here since RNA-Seq is inherently a relative quanitifcation method so this will always be an issue. IMO, use DESeq2::varianceStabilizingTransformation(), DESeq2::rlog() or limma::voom() after terminus and rank your transcripts that way.
Just keep the inherent transcript incertainties in mind.