Estimate the length of poly-A tails from randomly-primed RNAseq data
Can’t be done. If you already sequenced then I’m afraid the money is wasted (unless of course the data is good for something else).

The standard Illumina basecaller doesn’t deal well with homopolymers and will consequently call incorrect poly(A) lengths.

Amongst others, Narry Kim’s lab developed a dedicated method — TAIL-seq — to solve this problem. It’s a protocol for library prep using pulldown of biotin tagged tails (rather than random priming), plus dedicated basecalling software that uses spike-ins for calibration.

Be warned though: the protocol is reportedly technically challenging, and in order to use it you need an Illumina machine that gives you access to the raw image files before basecalling. Up-to-date Illumina machines won’t give you these files, full stop. So you’ll need to find a machine that runs an outdated firmware.