This is not a continental European republican system.
The G.G. does what the P.M. advises lest he wants a constitutional crisis. And as far as appointing the government, he's not like an elected president, who waits for the first elected person to come to him with proof that he/she can form a government. The G.G. has no such choice to make: He must first ask the party with the most seat to form a government. If, and only when, that government is defeated on a confidence vote will the G.G. have the option of asking the next party with the most seats to form a government instead of dissolving Parliament again - but he cannot do so against the advice of his then P.M. or he'll trow the country into a constitutional crisis, as happened the last time a G.G. tried to pull something like that (early 30's if memory serves).
So, regardless of all the "coalition" politics-speak out there, another minority PC government would have some life because it would have meant that:
1- it is still the party endorsed by the most voters;
2- these voters obviously have no problem with the proposed budget;
3- these voters did not perceive any of what the government did as "contemptuous" of Parliament; and,
4- the opposition parties would self destruct if they risked sending the country into another election too quickly on the flimsy hope that the G.G. would ask a coalition to govern regardless of the P.M. advice to dissolve Parliament (which, I am sure would be the advice).
Just my $0.02.