You should apply for the LTD regardless and contact an employment or ERISA attorney. I handle claims of that nature as well.
There are many attorneys who handle disability claims. The important part is to get one who focuses on fighting insurance companies, not dealing with the SSDI bureaucracy. Make sure they know ERISA as well.
I know from personal experience, and from talking to other attorneys who have worked on these claims, that Walgreen's disability plans are a mess. The company can't keep their story straight about what Plan documents apply to whom, what are the controlling terms of the Plan, etc. There are at least two different Plans (one for store managers, one for pharmacists and nurses, maybe a third one for other people). The STD is a payroll practice, as you figured out, and the LTD was at one point insured by MetLife, but as of around 2007 Sedgwick took over administration of the LTD in addition to the STD, which would suggest that LTD may be self-insured by Walgreen's now, as well (Sedgwick only does administration, not insurance).
Basically, this company's plan is a mess and you certainly need to seek an attorney. The STD may indeed be too little money to interest anyone, but if you have a good medical case, I can't imagine why anyone wouldn't work on your LTD case right now. OK, so Walgreen's refuses to take an LTD application - that may be proper under the terms of the LTD Plan or it may not. Either way, if you can effectively show that they won't consider your claim, exhaustion of administrative remedies is excused by virtue of futility and you can go directly to Court. In a recent case in Michigan, someone argued exactly that and not only did the Court order the rest of the STD paid up, he also ordered the LTD paid through the date of the Court's decision. Of course, the same Court denied a similar case only a week earlier. The law is not an exact science.
Look around here on Avvo or on the internet generally for an ERISA attorney you're comfortable with and then go talk to him or her. You don't necessarily need to limit yourself to your local area. ERISA is a Federal law that's basically the same all across the country, so you can pretty much talk to anyone you like. Attorneys from outside Ohio might have to jump through a hoop or two to get permission to represent you, but that's usually not too difficult.
Jeremy Bordelon is a licensed attorney in the State of Tennessee only, and is authorized to practice in all Tennessee State and Federal courts, and before the Social Security Administration in any jurisdiction. The answers provided on Avvo.com are for information purposes only, and should not be relied on as legal advice. This answer does not create an attorney-client relationship between us. In some jurisdictions, this answer may be construed as attorney advertising.