It depends on what you describe as reasonably cheap?
Insurer's are generally wary of young (male) drivers in fast modified cars as it is a toxic mix in terms of their claims statistics.
Have you considered a "family" multi-car policy with other family members in the same household?
These insurer's tend to treat the association of multi-cars and other family members as being statistically more responsible.
If you were to accept a significant voluntary excess and have some no claims history, this should help?
The other option might be to seek out a "classic car" limited mileage policy depending on your planned mileage?
It is important to disclose the modifications otherwise people can discover the insurance invalid.
Might it not be cost effective, to reverse one or two of the mods - such put back the original chip etc?