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My code has been adapated from Code for monthly NDVI medians in Google Earth Engine to calculate average sst by month and year

var sst = ee.ImageCollection('NASA/OCEANDATA/MODIS-Aqua/L3SMI')
.select('sst')
.filterDate(ee.Date('2013-01-01'), ee.Date('2017-12-31'))

var months = ee.List.sequence(1, 12);
var years = ee.List.sequence(2013, 2017);

var byMonthYear = ee.ImageCollection.fromImages(years.map(function(y) {
return months.map(function (m) {
  return sst
    .filter(ee.Filter.calendarRange(y, y, 'year'))
    .filter(ee.Filter.calendarRange(m, m, 'month'))
    .mean()
    .set('month', m).set('year', y);
    });
    }).flatten());
 print('byMonthYear', byMonthYear)

I simply want to a) export this data as a table, and b) plot this data by monthly mean over different years, similar to the DOY series in this guide.

For a) From the GEE guide I used this code for the table. However, the table in tasks spends a long time initializing and never resolving.

// Make a feature without geometry and set the properties to the dictionary 
of means.
var feature = ee.Feature(null, byMonthYear);

// Wrap the Feature in a FeatureCollection for export.
var featureCollection = ee.FeatureCollection([feature]);

// Export the FeatureCollection.
Export.table.toDrive({
collection: featureCollection,
description: 'BIOT_sst',
fileFormat: 'CSV'
});

For b) I've yet to find a way to plot different years without using the DOY series which isn't applicable here.

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