If btc change is supposed to be distributed to change addresses, can the distributed change be pooled and paid together in 1 new transaction?
a transaction has 1 source address


That is not correct.  A transaction may have any number of inputs, so it can spend the results of any number of previous transactions involving any number of addresses.  See https://en.bitcoin.it/wiki/Transaction.

Here is an example of a transaction with 4 inputs.

If you want to make a large payment using transactions from your 30 different addresses, you can make a transaction with 30 inputs.  Your Bitcoin wallet will handle this for you; if you try to make a payment of a larger amount than any single previous transaction contains, it will automatically select as many transactions to use as inputs as are needed.

Each additional input makes the transaction larger, and fees are based on the size of a transaction, so a transaction with 30 inputs will require a higher fee than one with 1 input.  However, it should be less than the fees to make 30 separate transactions.