As in so many areas of real estate typical doesn't typically apply. CRE lease commissions tend to vary depending on where the property is located across the nation. As you've mentioned they do tend to run the rates you quoted of 3-6% for the aggregate lease value of the lease for the first five year tiering downward for the next five, and then so on a so forth for extended lease terms.
You mention you're working on a lease renewal so immediately the question that comes into play is does the originating brokerage have claim to a renewal commission?
The next question is why are you being represented by a brokerage on a lease renewal? If its because you're unfamiliar with CRE leases, I get it. However, the pure essence of having a broker involved means you're opening up a commitment to pay when you could have eliminated the need to pay any commission by representing yourself with an existing tenant.
Brokers typically earn their commission for the heavy lifting work of finding tenants or buyers and then getting them interested in certain property's, not necessarily for "transacting", assuming they are knowledgeable about the marketplace.
Assuming the originating brokerage doesn't have a claim to a commission then my suggestion would be to use the mere fact you brought the two most important aspects of the transaction to the table, the tenant and the landlord, and you're willing to pay a commission (the tenant rep side and or landlord side) which is roughly half of a full commission typical for your marketplace. Then, try negotiate terms based on the premise you've made it easy for the broker to "transact", by bringing the parties to the negotiating table, and you want to pay the commission on terms amenable to both them and you.
If you get the 1/2 a commission part accepted I wouldn't push for terms. Pay the fee and move on. Here's why, the tenant already exists at the property which means the property owner has already accepted the tenants credit worthiness to lease the property (if you're a subsequent new owner you had a chance to review credit during your due diligence, if you didn't then that is on you). However, you can use the renegotiation process to get updated financial statements and then if financial condition has deteriorated since the originally lease use that information as a negotiating chip to throw on the table when the time is appropriate, assuming their financial condition is still acceptable.
Note: if you question whether a former brokerage has a claim to commissions (they do not necessarily have to be actively involved in a subsequent transaction to have such a claim) my suggestion would be to stop moving forward with lease extension negotiations until you're able to clarify who is owed what by whom and when.