I have worked for a private firm for four years and the State DOT for another eight. I've done highway design, structual design, planning, bridge inspection and the last couple of years in construction. One thing I found the same between working for the Agency and the Private Firm is exactly what you described - total lack of a training / mentorship program. My opinion of it is - you need 6-8 years of handholding and spoonfeeding someone before they even begin to be worth their salt. That's just the way it is in our field. So if you have an engineer and you actually want him to make money for you this is the investment you need to make in him or her.
Higher ups, MBA types and business owners often forget this as their entire mentality is shifted when they go through that MBA program. Not that its "wrong" the way many of them do things, or that the philosophy they embrace is wrong (they're doing something right or they wouldn't be turning a profit) but I find it is definately more contract oriented and less big picture oriented. Developing staff is always going to be second to just fulfilling the Contract so we can get paid and move onto the next one. If the client or Agency is willing to accept the product being turned out - must be you don't need any training. I disagree with it but that's how I find most managers think when it comes to training. Unless there is some certification that's need to bid on a job they do not pursue or even encourage staff to get it. That's why you'll find if you get into Contract Management - most outfits only care about "billable hours." We don't care about turning out the best product, or even a satisfactory product - we only want to make sure every guy on the books gets reimbursed to us hour-for-hour by the client. Most Consultants around here foam at the mouth for the opportunity to hire NICET inspectors because its easy money.
...At least in my experience. So yes, I agree and feel for your situation.
The good news for me, my Agency has actually put me in charge of training about 4 years ago. Since then I have put training packages together mainly for people in Construction that do the following jobs:
Engineer-In-Charge (Resident Engineer / Project Engineers)
Office Engineers
Inspectors
I start with the basics and cover the software they need to use then onto specific tasks they need to do. So how to inspect pile driving, concrete placement or paving operations; how to run an office; how to survive an FHWA audit; how to do as-built plans; how to get what you need off CADD; how to use an RTK Survey Rover in the field and so forth.
Thankfully the Agency has seen the light. We are failing audits and loosing Federal money. We are getting yelled at by the AGC to get more timely with payments and change orders. We have people in the field that have absolutely no idea what they are looking at. I am far from an expert on everything but the days are long gone where we had enough veteran staff availible to spoonfeed new people. When it was 6 veterans to every new person they could get all this training by mirroring a veteran. Now the ratio is 1 veteran to every 3 new people and it simply isn't sustainable. Now as time progresses the new people are put in charge of running projects in design and construction without the first clue. And it's evidenced with the outaregous overruns, overdue completion dates and exceptionally poor quality of the Plans and Proposal. So now we have a training program. It's argueable that before we didn't "need" one...but when management fails to keep the ranks filled in a timely fashion then you have the problem. You can't wait until after the mass exodus of retirees to decide you want to hire.
So enough about that. To your request for help - I can certainly forward you any training materials I have. Much of it is Agency specific so you'll have to read between the lines but I agree with everything Road Guy has said. Doesn't much matter where you go, the fundamentals are always the same. Free Floating screeds on modern asphalt pavers haven't changed a whole lot since the 1920's. You'll need to master:
1) Specifications - Requirements, Materials, Method of Measurement, Basis of Payment
2) Core Operations - HMA Placement, PCC Placement, Foundations, Steel Structures, PCC Structures, Drainage, Guide Rail, Overhead Signs, Maintainence
3) Agency Specific Manuals - Highway Design Manual, Steel Manual, Pavement Design Manual, CADD Standards, Prestressed Concrete Manual, Bridge Manual
Almost all this stuff is availible from the Agency. They have to make it availible for Consultants. Some have it all online in PDF form. Depending on what State your doing work for, you are going to want to be careful about only using national Standards. While many Agencies cut / paste from the AASHTO publications, many times there is additional State specifics. Always consult the governing guidance. Get the Engineering Bulletins / Engineering Instructions / Engineering Directives. Usually a project when awarded has a cut-off date for the last set of Standard Revisions are included. Make sure you design & build using the Specifications in the Contract (which may or may not be the latest and greatest). For example the last bridge I designed we used the older LFD because that's what they wanted - the new LRFD that has some differences.
Send me a PM with specifics and I'll try and help how I can.
Thanks,
-Mike
Best of luck. 
