I agree that you're probably looking at a hung parliament or narrow Labour majority. In Labour's favour, and contrary to some early accounts, Labour narrowed the Tories' support in the polls during the 1979 election from 50% to 43% and Callaghan was consistently more popular than Thatcher. So I wouldn't take the 1978 polls as gospel and think that Labour could have done better and secured a majority.
I disagree with the optimism about a continued Callaghan government - an election delays the Winter of Discontent due to union support but a similar event in 1979-80 is highly likely as government attempts to restrain pay had reached breaking point and a new generation of union leaders was less willing to compromise. The failure crushed Callaghan OTL and it's difficult to see what meaningful action the government could take at this point other than to muddle through and tolerate a return to the inflation of the Heath period. I can't see Callaghan securing support from his party for trade union reforms. North Sea Oil will help with balance of payments but at the expense of the exchange rate and industry, so possible that unemployment continues to rise slowly, but not reaching quite the heights it did under Thatcher. IIRC Callaghan had plans for Owen to be Chancellor and Healey Foreign Secretary if Labour won an election, and also proposed splitting the Treasury into two separate finance and economic ministries.
Conservatives probably win comfortably in 1982-83, either under Thatcher if she can hang on or Whitelaw. Perhaps even Heseltine but that may be wishful thinking as he was never hugely popular in the parliamentary party.