If this 'very big chain' is who I think it is, then I think you should be OK. I realise time may be important with price rises, but they generally have to get everything confirmed with their ticket office (which you normally don't have access to anyway). If everything is OK, and you've given the go-ahead, then they may take a day or 2 to do the taxes and so forth.

Did you work out the route or did you TA work it out? With some basic reading and help from the experts here, I suggest you work out the route, make sure it's OK. Once that's done, just say to the TA, book this by this date. If not, just go to another company or just another branch.

For your circumstances, I suggest you check progress with another agent (at the same branch) on Monday (or even today). Then do the rest ASAP, and make it clear to the agent that you want it on the quick.

(I'd a similar situation earlier when I booked my ticket. I wanted to avoid the most recent round of fuel surcharge, so I hurried my process and told my TA to ticket it ASAP. From there, it was done in about 2 days. I told my TA to hurry it up due to the surchage coming in, she didn't have a problem with that. Now, your circumstance is slightly different, I think it's the base price that's changing, so I don't know whether it'll affect the agent's commission. So be careful...)