Interim Response: We salute you in the most enthusiastic terms for your resolve to do the right thing. According to halacha, you certainly are not required to pay someone who is willing to forgo payment, at least for now. However, business ethics is a matter that needs strengthening, and it is important to conduct oneself properly even when there is an excuse not to, including that the money can be used for good things. If more people would think like you (hopefully, many already do and/or will soon), we could look forward to having Jewish businessmen referred to as “devout, ethical Jews.” We trust HaShem to enable us to support our families despite, or actually, because of the fact that we do not work on Shabbat, we pay for Jewish education, and we make other financial sacrifices in order to live by the Torah. In the same spirit, we should sanctify His Name by doing the morally right thing and trust Him to enable us to survive and even prosper in this world and receive our ultimate reward in the World to Come. Pragmatically speaking, as well, a reputation for integrity is a good asset, which you deserve.
We need to clarify the following before answering:
Do you serve as a middleman between clients and consultants, or do you hire the consultants on your own and include their charges in your total fee?
Do you make any stipulations with your consultants about payment conditions?
Are there clear standards among architects and engineers regarding cases of partial payment or non-payment by a client?
Do you feel you were at all negligent in your handling of the work done by the engineers and the preparation of the client for the possibility of a larger than expected charge? If so, how?

Question (Part II): The engineers and I have no written or even detailed oral agreement, but we both assume to be working within the accepted practice. The American Institute of Architects (AIA) told me that their standard contract states that the architect should pay the consultants according to the percentage of money received from the client and diligently pursue the remainder of the payment. They provided no information to fit this exact case.

Answer (Part II): Your responsibility to subcontractors is as an agent and, thus, you are not required to compensate them out of your pocket when a client refuses to pay. This is confirmed by professional practice and by the AIA standard contract.
The client was required to pay you, partly on your own behalf and partly on the engineers’ behalf. When one receives partial payment in such an arrangement, how is the money to be allocated? The Shulchan Aruch‎{&&}‎ rules that a creditor who receives payment which suffices only for one of two debts from a single debtor has the authority to determine to which debt the payment relates, even if the determination differs from the intention of the debtor. The Rama‎{&&}‎ applies this even to a case where someone else was the creditor of the second debt. Thus, halachically, in the absence of pertinent accepted practice, you would have been able to keep the entire payment for your architectural services. However, this is not always the right thing to do.
Furthermore, your case differs from the standard one in the following way: An agent who arranges that A will work for B can obligate himself to pay A personally for the work done.‎{&&}‎ While this is not fully the case in your situation, it is so partially. The AIA contract obligates the architect to give his consultants a proportional share of the funds received. As you accept this contract as the fair industry standard, it is as if you agreed explicitly to forgo your right to keep all of the payment.
There is another element to consider. Although we learned that the collecting creditor can determine the complex payment’s nature, the debtor’s stated preference is relevant to the desired, ethical determination. Specifically, although convention does not allow you to demand payment for yourself first, if it is the client who refuses to pay the consultants, it seems logical that you could accept payment for yourself in the meantime. (A clear, public ruling of the AIA to the contrary would overrule our logic.)
At first glance, this is your situation, as your client feels that he has gained from your work but not significantly from the engineers’ work. However, upon further consideration [Editor’s Note – the description of the case is abridged], this seems to be an oversimplified perspective. The client does not seem to question the quality of the engineers’ work, rather the broad mandate they were given or took upon themselves to investigate engineering issues beyond the client’s interest, and he blames you at least partially for this.
For our purposes, it is important to know how the client would answer the following questions, regardless of whether he is right in his thinking.
Did you intend that the payment should go to the architect and that the engineers should receive little or nothing?
Alternatively, do you feel that the total amount paid represents the value of services rendered, that neither the architect nor the engineers acted properly, and so they should be left to figure out how to divide the money?
If the latter is true, as it sounds, then the AIA standard that the architect should not take a proportionally higher percentage of the payment than the engineers is again pertinent; you would essentially be splitting the loss and, while you both might be disappointed, you would both receive some compensation for your efforts. If the client’s refusal to pay in full is simply a disingenuous excuse, then the AIA standard again applies, as the supposed payment for only one service is actually a partial payment for both.