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The Murchison Widefield Array (MWA) is a low-frequency aperture array capable of high-time and frequency resolution astronomy applications such as pulsar studies. The large field-of-view of the MWA (hundreds of square degrees) can also be exploited to attain fast survey speeds for all-sky pulsar search applications, but to maximise sensitivity requires forming thousands of tied-array beams from each voltage-capture observation. The necessity of using calibration solutions that are separated from the target observation both temporally and spatially makes pulsar observations vulnerable to uncorrected, frequency-dependent positional offsets due to the ionosphere. These offsets may be large enough to move the source away from the centre of the tied-array beam, incurring sensitivity drops of $\sim$30-50\% in Phase II extended array configuration. We analyse these offsets in pulsar observations and develop a method for mitigating them, improving both the source position accuracy and the sensitivity. This analysis prompted the development of a multi-pixel beamforming functionality that can generate dozens of tied-array beams simultaneously, which runs a factor of ten times faster compared to the original single-pixel version. This enhancement makes it feasible to observe multiple pulsars within the vast field of view of the MWA and supports the ongoing large-scale pulsar survey efforts with the MWA. We explore the extent to which ionospheric offset correction will be necessary for the MWA Phase III and the low-frequency Square Kilometre Array (SKA-Low).