An influential US lobbying network of Republican politicians and big businesses is seeking to avert a looming funding crisis by appealing to major donors that have abandoned it over the past two years following criticism of its policy on gun laws.

The Guardian has learned that the American Legislative Exchange Council (Alec), which shapes and promotes legislation at state level across the US, has identified more than 40 lapsed corporate members it wants to attract back into the fold under a scheme referred to in its documents as the "Prodigal Son Project".

The target firms include commercial giants such as Amazon, Coca-Cola,General Electric, Kraft, McDonald's and Walmart, all of which cut ties with the group following the furore over the killing of the unarmed black teenager Trayvon Martin in Florida in February 2012.

Alec was embroiled in the controversy surrounding Florida's 2005 "stand-your-ground" law under which George Zimmerman, the neighbourhood watch volunteer who shot and killed the 17-year-old Martin, initially claimed self-defence. The Florida law was picked up by Alec, and, working in partnership with the National Rifle Association, used as a template for one of its "model bills", which was then taken up by other states across the country.

The Guardian has learned that by Alec's own reckoning the network has lost almost 400 state legislators from its membership over the past two years, as well as more than 60 corporations that form the core of its funding. In the first six months of this year it suffered a hole in its budget of more than a third of its projected income.

The reference to the Prodigal Son Project is just one of many revelations contained in a batch of internal Alec documents that have been obtained by the Guardian. The documents, prepared for its most recent annual board meeting in Chicago in August, cast light on the inner workings of the group.

They show that:

• Alec has set up a separate sister group called the "Jeffersonian Project" amid concerns over possible government inquiries into whether its activities constitute lobbying – which would threaten its tax-exempt status;

• the network has suffered a decline in its membership among state-based Republicans and among big corporations following the Trayvon Martin controversy;

• its income raised from conferences, membership fees and donations has fallen short, leaving the group with a potential funding crisis;

• a draft agreement prepared for the board meeting proposed that Alec's chairs in each of the 50 states, who are drawn from senior legislators, should be required to put the interests of the organisation first, thus setting up a possible conflict of interest with the voters who elected them;

• Alec also considered extending its remit to include the gambling industry, particularly online gambling, as a possible source of new members and revenue.

Alec reconvenes for its next nationwide meeting, described as a "states and nation policy summit", on Wednesday in Washington. The three-day event will be attended by hundreds of state legislators and corporate representatives.

In a sign of the influence the network holds with Republicans, it will be addressed by rising stars of the party including US senator Ted Cruz of Texas, who led the push for the recent government shutdown, and the party's budget guru, Paul Ryan of Wisconsin.

The network also counts among its former members the two highest ranking Republicans in the House of Representatives, John Boehner and Eric Cantor, as well as prominent Republican governors such as Scott Walker of Wisconsin and John Kasich of Ohio.

The documents seen by the Guardian show that Alec is hoping to avoid legal, tax and ethical challenges by creating a separate sister organisation it calls the "Jeffersonian Project". The new body would be categorised as a 501(c)(4) social welfare organisation, a designation that would allow Alec to be far more overt in its lobbying activities than its current charitable status as a 501(c)(3).

"Any activity that could be done by Alec may be done by Jeffersonian Project if legal counsel advises it would provide greater legal protection or lessen ethics concerns," a note on the proposed new body to Alec's board of directors says. The note adds that the Jeffersonian Project would remove "questions of ethical violations made by our critics and state ethics boards and provides further legal protection".

Alec's critics have accused it of violating tax laws by lobbying on behalf of rightwing legislation that advances the interests of its corporate members. Among the areas that Alec has pursued aggressively in the form of model bills are measures to privatise public education, cut taxes, reduce public employee compensation and workplace rights, oppose Obamacare and resist state action to reduce global warming gas emissions.

A letter included among the documents from Alec's lawyer, Alan Dye, warns that "though we do not believe that any activity carried on by Alec is lobbying, the IRS could disagree". It also makes clear that major potential donors are holding back because they are anxious about Alec's tax status.

"Alec has been approached by donors who are willing to make sizable donations, but insist that the donations go to a section 501(c)(4) organization," Dye writes.