Does a high +∆G mean that the reaction is irreversible (and equilibrium cannot be attained) or that the reaction lies to the right?

Reactions are spontaneous when the change in free energy (∆G)is negative. (spontaneous does not imply rate, only favored direction).
Since ∆G = ∆H- T∆S, reactions tend to be favored if the change in enthalpy (∆H) is negative (exothermic reaction, goes to lower potential energy), and the change in entropy (∆S) is positive (system increases in disorder,)
If ∆H is negative and ∆S is positive, the reaction is spontaneous at all temperatures.
If ∆H is positive and ∆S is negative, the reaction is never spontaneous.
If both ∆H and ∆S are negative the reaction may be spontaneous at low temperatures, but when T∆S becomes greater than ∆H, reaction will no longer be spontaneous.
If both ∆H and ∆S are positive, the reaction will become spontaneous when T∆S exceeds ∆H.

I think you've got it mixed up.

Large positive `DeltaG` indicates a nonspontaneous reaction (i.e. the reverse direction is very fast), which is irreversible in the REVERSE direction, not forward direction.

Equilibrium reactions necessarily have `DeltaG = 0`, so equilibria cannot lie to either side AND be irreversible at the same time.

[You may want to read this for further discussion on irreversibility.](https://socratic.org/questions/for-a-spontaneous-process-in-an-isolated-system-the-change-in-entropy-is-positiv#532832)

Consider the deviation of the change in Gibbs' free energy `DeltaG` from standard state:

`DeltaG = DeltaG^@ + RTlnQ`

• First of all, reactions that have positive `DeltaG` are necessarily nonspontaneous, and therefore, the forward direction is easily reversed.

Thus, the reactants have a really hard time reaching a dynamic equilibrium (where `r_(fwd) = r_(rev)`), whatever the size of `bbQ` happens to be, since the reverse rate is much larger than the forward rate, i.e. `r_(fwd)` `"<<"` `r_(rev)`.

• Second, all spontaneous reactions are irreversible... in the forward direction. Therefore, `DeltaG` must be negative for irreversible forward reactions. In that case, `r_(fwd)` `">>"` `r_(rev)`.