combining section 121 gain and 1031 exchange

[Tatyana Shevnina]

When combining section 121 gain and 1031 exchange, can you take out the section 121 gain or does it have to be included in the cost of the replacement property?

For example, relinquished property is sold for $800K with $600K capital gain, where $500K qualifies for 121 exclusion and $100K is deferred via 1031 exchange. Can you take out $500K tax free and buy a replacement property for $300K? Or do you still need to reinvest the full $800K into the replacement property? I omitted closing costs, etc. for simplicity. 

In prior threads, @Dave Foster (can't tag for some reason) mentioned that section 121 gain is boot, but ultimately becomes tax free once 121 exclusion is applied. From that I gathered that $500K can be taken out tax free. Wanted to double check that my understanding is correct.

Thanks in advance!