Are Chebyshev Type 1 filters very unstable at very high orders?
With infinite-precision arithmetic they will be stable. However, since you don't have infinite-precision arithmetic, you will have quantization issues even if you use 64-bit precision. These quantization issues can make your filter unstable. Even if your filter is stable, perhaps you will not get the frequency response wanted because of these quantization issues.

First solution : split your order-30 IIR filter into 15 order-2 IIR filters and cascade them. This should fix your problem.

https://www.dsprelated.com/freebooks/filters/Series_Second_Order_Sections.html
https://www.mathworks.com/help/signal/ref/tf2sos.html

Alternatively : Instead of cascading, you can parallelize the order-2 IIR filters.

https://www.dsprelated.com/freebooks/filters/Parallel_First_and_or_Second_Order.html

Finally, do you really need an order-30 chebyshev filter? I find it hard to believe to you really more than an order-8 or order-10 IIR filter. 

Edit : You edited your post to mention that you already use biquads. Have you tried an simpler filter, like an order-4 IIR? Make sure it works for an order-4 IIR filter (i.e. 2 cascaded biquads) and then try increasing the order. Also, are you sure that your factorization algorithm is correct? Maybe, there's a simple bug hidden somewhere and it will be easier to spot it with a reduced-order filter.