* Johnson says to submit proposals shortly
* Says Irish backstop will be removed from deal
* Ireland criticises earlier proposals
* Pro-Brexit lawmakers: We can vote for a deal (Adds details and context)
By Elizabeth Piper and Kylie MacLellan
MANCHESTER, England, Oct 1 (Reuters) - Britain will shortly present the European Union with proposals for an amended Brexit agreement, including ideas that remove the contested insurance policy for the Irish border that Britain previously signed up to, Prime Minister Boris Johnson said.
More than three years since the 2016 referendum, the United Kingdom is heading towards an Oct. 31 Brexit date without a clear understanding of whether it will leave with a deal, without a deal or even leave by that deadline.
Before the proposals were formally made, Ireland dismissed reported ideas including physical checks on goods at a distance from the border itself, with Foreign Minister Simon Coveney quipping: "Non-Starter".
"We've made a very good offer, we're going to make a very good offer, we're going to be tabling it formally very soon," Johnson, a leader of the "Out" campaign in the referendum, told the BBC.
"We do think there's a good way forward, we do think there's a good solution. I very much hope that our European, EU friends in Brussels, in Dublin, in Germany as well will want to take it forward."
Johnson says he wants to secure an amended agreement at an EU summit on Oct. 17-18, and that both sides are keen on a deal that could allow an orderly Brexit.
In a moment of truth that will define the future of Brexit and his premiership, Johnson is betting he can get enough concessions from Brussels to make an agreement acceptable to many Brexit supporters in the British parliament, which must ratify any deal.
If he succeeds, Johnson will go down in history as the British leader who delivered Brexit. If he fails, a law has been passed by parliament forcing him to delay Brexit -- a step that could destroy his popularity among "Leave" voters.
Ireland is crucial to any Brexit solution.
Johnson's gamble hinges on the removal of the backstop, an insurance policy which aims to avoid the reimposition of checks along what would be the United Kingdom's only land border with the EU, between Ireland and British-ruled Northern Ireland.
Maintaining an open border is seen by many on the island of Ireland and by the EU as important to safeguarding the 1998 Good Friday Agreement (GFA) that ended decades of sectarian violence in Northern Ireland.
"What we want to do is to get rid of the backstop, that is the most important thing," Johnson said, adding there was no point in leaving the EU only to stay locked in a customs union.
The Withdrawal Agreement that former Prime Minister Theresa May struck in November with the EU says the United Kingdom will remain in a customs union "unless and until" alternative arrangements are found to avoid a hard border.
Johnson said on Tuesday he didn't want to threaten the GFA.
But many British lawmakers oppose the prospect of being bound to EU rules and customs duties that would prevent Britain doing its own trade deals and leave it overseen by EU judges.
"We would like to be able to vote for a deal and actually I'm highly confident if Boris brings back a deal it will be a deal which he expects we'll want to support," said Steve Baker, chairman of the European Research Group of pro-Brexit Conservative lawmakers.
"If it's Brexit in name only, I will vote against it."
Under questioning, Johnson said there would have to be some checks on the island of Ireland -- a step too far for Irish nationalists. Dublin has also consistently said that the border must remain seamless.
"That's just the reality," Johnson said. "Because in the end, a sovereign, united country must have a single customs territory. When the UK withdraws from the EU that must be the state of affairs that we have."
Johnson denied a report by Irish broadcaster RTE that there would have to be border posts between 5-10 miles (8-16 km) back from the border.
Sinn Fein President Mary Lou McDonald said on Tuesday a reported proposal from Britain to set up "customs clearance centres" on both sides of the Irish border was absolutely not acceptable as it represented a hardening of the frontier.
"What we're coming up to now is, as it were, the critical moment of choice for us as friends and partners about how we proceed," Johnson said. (Reporting by Elizabeth Piper and Kylie MacLellan, Additional reporting by Kate Holton and Andy Bruce writing by William James and Guy Faulconbridge; Editing by Michael Holden and Catherine Evans)