Is LP distortion the record or the cartridge?

Dear @mglik  : Assuming that the head-amp along the Audible Illusions you owned were in good condition both units are not so bad enough to not reproduce the kind distortions you are talking about.

Assuming that you are loading the Shilabe with same or very near impedance value than in your former units then what you are experienced/listened could be generated inside your new unit or if by coincidence when you connected the new unit the Shilabe started with a suspension " problem " or a stylus tip " problem .

If I was you I will look probably with an audio friend that permits to mount your Shilabe and listen to it and if not distortion at all then your new phono stage has a trouble and you need to know it even if with the Lyra does not happens. Is up to you.

R. 

The first thought is that the cartridge is not properly tracking. Am using a Miyajima Shalabi

@mglik How old is your cartridge?

The cartridge probably has about 2000 hours on it.
I am only getting that distortion on old and, probably, worn records.

Dear @mglik  : The kind of distortions you listened are a clear sign ( along those 2K play hours. ) that as I told you exist a " problem !" at the stylus tip.
The cartridge is showing you his degradation level that is at limit and needs retip it.

Even that in other LPs you don't listen yet any kind of similar distortions that cartridge is making an irreversible damage on all the LP grooves you play with it. My advise is to stop using it and wait for your Lyra.

R.

The cartridge probably has about 2000 hours on it.
I am only getting that distortion on old and, probably, worn records

Sometimes you can get dust buildup on the stylus tip that is difficult to see and difficult to clean off. If the stylus has just a little dirt on it distortion will be present! But if you are careful you can remove it with a good stylus cleaner. Have you tried this?