By nature, the radiation pattern of a small loop antenna will not be uniform in the azimuth. It will typically have the classic bipolar lobe pattern with nulls in the quadrature positions as shown in your plots.
You should either consider classes of antennas that are omnidirectional in the azimuth (e.g. monopoles, vertical dipoles, horizontal slot, etc.) or phase two loops that are oriented 90 degrees from one another. In the latter case, the pattern will be pseudo omni in the azimuth and the solution will likely require two PCBs and an interconnecting transmission line.
You state that you require 2.5 dB gain. Note that this is an ambiguous statement since there is no normative reference. It should likely be stated as either dBi or dBd gain. In professional circles, dBi is used almost exclusively but it still should be explicitly stated.
Note that you also specified an RL without stating the ZO of the transmission line, the output impedance of the transmitter, or the input impedance of the receiver. All of which are essential facts in order to engineer a solution that fully meets the requirement.